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  <front>
    <journal-meta>
<journal-id journal-id-type="publisher">AMT</journal-id>
<journal-title-group>
<journal-title>Atmospheric Measurement Techniques</journal-title>
<abbrev-journal-title abbrev-type="publisher">AMT</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Atmos. Meas. Tech.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1867-8548</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>

    <article-meta>
      <article-id pub-id-type="doi">10.5194/amt-10-3499-2017</article-id><title-group><article-title>Consistency of aerosols above clouds characterization from A-Train active
and passive measurements</article-title>
      </title-group><?xmltex \runningtitle{Consistency of aerosols above clouds}?><?xmltex \runningauthor{L.~T. Deaconu et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Deaconu</surname><given-names>Lucia T.</given-names></name>
          <email>lucia-timea.deaconu@ed.univ-lille1.fr</email>
        <ext-link>https://orcid.org/0000-0002-2919-1491</ext-link></contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Waquet</surname><given-names>Fabien</given-names></name>
          <email>fabien.waquet@univ-lille1.fr</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Josset</surname><given-names>Damien</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Ferlay</surname><given-names>Nicolas</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Peers</surname><given-names>Fanny</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-2796-8738</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Thieuleux</surname><given-names>François</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Ducos</surname><given-names>Fabrice</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Pascal</surname><given-names>Nicolas</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Tanré</surname><given-names>Didier</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Pelon</surname><given-names>Jacques</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Goloub</surname><given-names>Philippe</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Université de Lille, CNRS, UMR 8518, LOA – Laboratoire d'Optique
Atmosphérique, 59000 Lille, France</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>US Naval Research Laboratory, NASA Stennis Space Center, 39529,
Mississippi, USA</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>College of Engineering, Mathematics and Physical Sciences, University
of Exeter, Exeter, UK</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>ICARE Data and Services Center, University of Lille, Villeneuve
d'Ascq, 59655, France</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>LATMOS, Université Paris, (CNRS-UVSQ), Paris 75005, France</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Lucia T. Deaconu (lucia-timea.deaconu@ed.univ-lille1.fr)
<?xmltex \hack{\newline}?> and Fabien Waquet (fabien.waquet@univ-lille1.fr)</corresp></author-notes><pub-date><day>22</day><month>September</month><year>2017</year></pub-date>
      
      <volume>10</volume>
      <issue>9</issue>
      <fpage>3499</fpage><lpage>3523</lpage>
      <history>
        <date date-type="received"><day>10</day><month>February</month><year>2017</year></date>
           <date date-type="rev-request"><day>13</day><month>March</month><year>2017</year></date>
           <date date-type="rev-recd"><day>20</day><month>July</month><year>2017</year></date>
           <date date-type="accepted"><day>1</day><month>August</month><year>2017</year></date>
      </history>
      <permissions>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
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<self-uri xlink:href="https://amt.copernicus.org/articles/10/3499/2017/amt-10-3499-2017.pdf">The full text article is available as a PDF file from https://amt.copernicus.org/articles/10/3499/2017/amt-10-3499-2017.pdf</self-uri>


      <abstract>
    <p>This study presents a comparison between the retrieval of optical properties
of aerosol above clouds (AAC) from different techniques developed for the
A-Train sensors CALIOP/CALIPSO and POLDER/PARASOL. The main objective is to
analyse the consistency between the results derived from the active and the
passive measurements. We compare the aerosol optical thickness (AOT) above
optically thick clouds (cloud optical thickness (COT) larger than 3) and
their Ångström exponent (AE). These parameters are retrieved with the
CALIOP operational method, the POLDER operational polarization method and the
CALIOP-based depolarization ratio method (DRM) – for which we also propose a
calibrated version (denominated DRM<inline-formula><mml:math id="M1" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>, where SODA is the
Synergized Optical Depth of Aerosols). We analyse 6 months of data over three
distinctive regions characterized by different types of aerosols and clouds.
Additionally, for these regions, we select three case studies: a
biomass-burning event over the South Atlantic Ocean, a Saharan dust case over
the North Atlantic Ocean and a Siberian biomass-burning event over the North
Pacific Ocean. Four and a half years of data are studied over the entire
globe for distinct situations where aerosol and cloud layers are in contact
or vertically separated. Overall, the regional analysis shows a good
correlation between the POLDER and the DRM<inline-formula><mml:math id="M2" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOTs when the
microphysics of aerosols is dominated by fine-mode particles of
biomass-burning aerosols from southern Africa (correlation coefficient
(<inline-formula><mml:math id="M3" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of 0.83) or coarse-mode aerosols of Saharan dust (<inline-formula><mml:math id="M4" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.82).
A good correlation between these methods (<inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.68) is also observed
in the global treatment, when the aerosol and cloud layers are separated
well. The analysis of detached layers also shows a mean difference in AOT of
0.07 at 532 nm between POLDER and DRM<inline-formula><mml:math id="M6" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> at a global scale. The
correlation between the retrievals decreases when a complex mixture of
aerosols is expected (<inline-formula><mml:math id="M7" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.37) – as in the East Asia region – and
when the aerosol–cloud layers are in contact (<inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.36). The
correlation coefficient between the CALIOP operational method and POLDER is
found to be low, as the CALIOP method largely underestimates the aerosol
loading above clouds by a factor that ranges from 2 to 4.</p>
    <p>Potential biases on the retrieved AOT as a function of cloud properties are
also investigated. For different types of scenes, the retrieval of
above-cloud AOT from POLDER and from DRM are compared for different
underlying cloud properties (droplet effective radius (<inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and
COT retrieved with MODIS). The results reveal that DRM AOT vary with
<inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. When accounting for <inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in the DRM algorithm,
the consistency between the methods increases. The sensitivity study shows
that an additional polarized signal coming from aerosols located
<italic>within</italic> the cloud could affect the polarization method, which leads
to an overestimation of the AOT retrieved with POLDER algorithm. In addition,
the aerosols <italic>attached</italic> to or <italic>within</italic> the cloud can potentially
impact the DRM retrievals through the modification of the cloud droplet
chemical composition and its ability to backscatter light. The next step of
this work is to combine POLDER and CALIOP to investigate the impacts of
aerosols on clouds and climate when these particles are transported above or
within clouds.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p>By interacting with radiations and by modifying the cloud reflectivity and
microphysics, aerosols have important impacts on the Earth's radiative budget
and water cycle (IPCC, 2013). These atmospheric particles absorb and scatter
the sunlight, resulting in the so-called direct radiative effect (DRE).
Although aerosols always produce a cooling effect at the Earth's surface, the
sign and the amplitude of the DRE of aerosols at the top of the atmosphere
depend not only on the aerosol properties but also on the reflective
properties of underlying surface. For instance, in cases where absorbing
aerosol layers are located above clouds, the DRE of aerosols is predominantly
positive as a result of the reduction of the local planetary albedo (Keil and
Haywood, 2003). By absorbing sunlight, aerosols also warm the layer of the
atmosphere where they reside. This modifies the vertical profile of
temperature in the atmosphere, which may affect the process of evaporation
and cloud formation. This effect is called the semi-direct effect (Hansen et
al., 1997; Ramanathan et al., 2001). Aerosols also impact the cloud
properties by acting as cloud condensation nuclei and ice nuclei. They may
modify the cloud microphysics and cloud brightness with potential impacts on
precipitation and cloud lifetime (Rosenfeld, 2000; Twomey, 1974). These
effects are referred as aerosol indirect effects and tend to cool the Earth.</p>
      <p>The lack of knowledge of aerosol properties in cases of scenes of aerosols above clouds
(AAC)  has been recently highlighted as a source of uncertainty for the
estimation of all-sky DRE of aerosols (Peers et al., 2016). Different
approaches have been developed to quantify the DRE of AAC using satellite
observations (Chand et al., 2009; Feng and Christopher, 2015; Meyer et al.,
2013). But despite recent observational and modelling studies (De Graaf et
al., 2014; Peers et al., 2015, 2016; Zhang et al., 2016), the aerosol DRE for
AAC remains a subject of large uncertainty. In the process of quantification
and interpretation of the aerosol impact on climate, the aerosol interactions
with clouds constitute the largest uncertainty in global climate models
(Myhre et al., 2013a, b). The study of AAC may also contribute to reduce
those uncertainties. For instance, in case of absorbing AAC, the warming of
the atmosphere occurring above stratocumulus clouds might reduce the strength
of the convection and consequently impact the vertical development and the
cloud properties. This warming might inhibit the entrainment of dry air at
the top of the cloud, preserving the humidity of the cloud and increasing the
liquid water content and the persistence of clouds (Johnson et al., 2004;
Wilcox, 2010). Evidence of the first indirect effect was also found over the
South Atlantic region, where AAC events are frequently observed. Costantino
and Bréon (2013) notably found a strong decrease in the droplet effective
radius when the aerosol layers are in contact with the top altitude of the
cloud deck.</p>
      <p>The scientific community is working on better monitoring the load and
microphysical properties of AAC in order to assess the influence of those
particles on the Earth's radiative budget and clouds. The constellation of
satellites called the A-Train provides different passive and active sensors for
monitoring clouds and aerosols
(<uri>http://atrain.nasa.gov/publications/A-TrainFactSheet.pdf</uri>). Passive
imagers offer larger spatial coverage but have no direct information of the
vertical distribution of particles in the atmosphere. Active methods offer
unique capabilities, complementary to the passive methods, and are dedicated
to the study of the vertical profiles of clouds and aerosols. The main
retrieved optical properties for aerosols, in “clear-sky” conditions, are
the aerosol optical thickness (AOT) and the Ångström exponent (AE),
which is a parameter indicative of the particles size (Kaufman et al., 2002).
Recent methods also allow retrieving the aerosol single scattering albedo
(SSA) over clear-sky ocean scenes (Torres et al., 2013; Waquet et al., 2016).</p>
      <p>The active sensor Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP)
installed on CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite
Observation) satellite provides high-resolution vertical profiles of aerosols
and clouds (Chand et al., 2008; Winker et al., 2010). CALIOP provides the
total attenuated backscatter signal (km<inline-formula><mml:math id="M12" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> sr<inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> at 532 and
1064 nm. From the backscatter measurements, an operational aerosol algorithm
allows for retrieval of the vertical extinction profiles as well as the AOT
in clear and cloudy skies by assuming an aerosol lidar ratio (extinction to
backscatter) (Omar et al., 2009; Young and Vaughan, 2009). Moreover, two
orthogonally polarized channels measure the parallel and perpendicular
backscatter signal at 532 nm that allows calculating the depolarization
ratio (i.e. the ratio of the two orthogonal polarization signals) (Hunt et
al., 2009). Depolarization measurements are used for discrimination between
spherical and non-spherical particles (Sassen, 1991). CALIOP provides
exhaustive details on the vertical distribution of optical and microphysical
properties of aerosols and clouds, including their shape, and a qualitative
classification of aerosol type (via the wavelength dependence of the
backscatter) (Winker et al., 2009; Young and Vaughan, 2009).</p>
      <p>Alternative CALIOP-based research methods have also been introduced to
retrieve above-cloud AOT (ACAOT). The depolarization ratio method (DRM) (Hu
et al., 2007a) and the colour ratio method (CRM) (Chand et al., 2008) use
fewer assumptions for the retrieval of aerosol properties. These methods are
based on light transmission methods and treat the liquid water clouds
situated underneath the aerosol layer as a target. Hu et al. (2007b) have
shown that, in the case of opaque water clouds, the layer-integrated
attenuated backscatter at 532 nm and layer-integrated attenuated
depolarization ratio at 532 nm can be used to retrieve the aerosol optical
depth of the overlaying aerosol or optically thin cloud layers. The CRM uses
the layer-integrated attenuated colour ratio, which is the ratio of integrated
attenuated backscatter at 1064 to 532 nm. Over the visible to near-infrared
spectral region, fine-mode absorbing aerosols above clouds exhibit a strong
wavelength dependence colour ratio (Chand et al., 2008). This makes possible
the detection of absorbing biomass-burning aerosols transported above clouds.
The colour ratio observed in the case of coarse-mode particles or purely
scattering fine-mode aerosols transported above clouds exhibits little or no
wavelength dependence and, thus, these particles can be less accurately
detected with the CRM method.</p>
      <p>Passive sensors have also been used to obtain information on aerosols above
clouds. For example, Torres et al. (2012) have developed an algorithm to
retrieve the ACAOT and the underlying aerosol-corrected cloud optical depth,
using radiance measurements performed in the ultraviolet (UV) by the Ozone
Monitoring Instrument (OMI). The method takes advantage of the ability of
biomass-burning and mineral dust aerosols to strongly absorb UV radiations.
Another method that can retrieve the ACAOT and, simultaneously, the
aerosol-corrected cloud optical thickness (COT) is the “colour ratio” method proposed by Jethva et
al.  (2013) that employs measurements in visible and shortwave infrared
channels from the Moderate Resolution Imaging Spectroradiometer
(MODIS). Also, Meyer et al. (2015) developed an algorithm that employs
reflectance measurements from six MODIS channels (from the visible to the
shortwave infrared) to retrieve the ACAOT, as well as the COT and droplet
effective radius (<inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of the underlying cloud.</p>
      <p>The multi-directional polarization measurements have shown sensitivity to AAC
scenes (Waquet et al., 2009; Hasekamp, 2010; Knobelspiesse et al., 2011).
The Polarization and Directionality of Earth Reflectances (POLDER) instrument is
measuring the directionality and polarization of light reflected by the
Earth–atmosphere system. The aerosols generate an additional polarized light
at forward and side scattering angles (70–130<inline-formula><mml:math id="M15" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>) and reduce the
polarized signal of the cloud bow (i.e. a strong polarized rainbow feature
observed near 140<inline-formula><mml:math id="M16" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> in scattering angle). Mineral dust particles do
not much polarize light, but they strongly minimize the cloud bow magnitude.
Based on these effects, Waquet et al. (2009) have developed a method for
retrieving the properties of aerosols above clouds that relies on the
polarized radiances measured by POLDER. Because polarized radiances are not
affected by the optical thickness of the cloud (i.e. the polarized radiance
reflected by the cloud is saturated when the cloud is optically thick
enough), the method is able to retrieve the scattering ACAOT at two
wavelengths (670 and 865 nm) without much assumption about cloud properties. An
analysis of the global results obtained with the operational algorithm is
given in Waquet et al. (2013a). Furthermore, Peers et al. (2015) have
developed a complementary method that uses additional total multidirectional
radiances measured by POLDER. The method provides the aerosol SSA and the
aerosol-corrected COT. So far, the algorithm of Peers et
al. (2015) is a research method, only applied for regional studies (Peers et
al., 2016).</p>
      <p>Jethva et al. (2014) performed an intercomparative analysis of the ACAOT
retrieved with the aforementioned methods in order to assess the consistency
(or lack thereof) between the two independently derived ACAOTs. The results were
encouraging and, despite the use of different assumptions and measurements, a
close agreement was reported over homogeneous clouds. Similar to this study,
our paper will focus on the comparison between collocated active and passive
AAC inversion products, improving our understanding of the ACAOT. But,
compared to Jethva et al. (2014), who focused only on two study cases, we
perform a global and multi-annual investigation to provide robust statistics
results. The vertical distribution of the aerosol and cloud layer will be
also considered. We will concentrate on the following methods: (a) the CALIOP
operational method (CALIOP<inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> because of the numerous studies in
which it was used, (b) the DRM developed by Hu et al. (2007a), (c) a
calibrated version of the DRM algorithm and (d) the POLDER polarization
method. The DRM and POLDER methods were chosen because both are measuring AAC
properties above the same type of cloudy scenes (i.e. optically thick and
homogeneous liquid water clouds). Moreover, both techniques are sensitive to
all types of particles (scattering or absorbing particles, fine or coarse
ones), which is not the case for CRM, which can operate only for absorbing
aerosols. It is also interesting to compare these two approaches since the
POLDER method requires a hypothesized aerosol microphysics, while DRM does
not require any hypothesis for the aerosols but does require assumptions and an
approximate model to estimate the signal backscattered by clouds.</p>
      <p>To begin with, we briefly recall the principle of each algorithm and the data
selection strategy. The results of AOT intercomparison are presented in
Sects. 3 and 4. We first present a regional comparison and then describe a
global comparison for a period of 4.5 years in function of the
type of aerosols and AAC scenes (aerosol and cloud layers in contact or well
separated). Discussions and conclusions will be drawn in Sects. 5 and 6.</p>
</sec>
<sec id="Ch1.S2">
  <title>Methodology and data selection</title>
<sec id="Ch1.S2.SS1">
  <title>POLDER polarization method</title>
      <p>POLDER, an instrument on the PARASOL (Polarization and Anisotropy of
Reflectances for Atmospheric Science coupled with Observations from a Lidar)
satellite, is a wide-field imaging radiometer/polarimeter
(Tanré et al., 2011). This instrument measures
the angular and spectral behaviour of the normalized total and polarized
radiances (Herman et al., 2005).</p>
      <p>The method for retrieving the above-cloud scattering AOT developed by Waquet
et al. (2013b) consists of a comparison between polarized radiances measured
by POLDER at 670 and 865 nm and polarized radiances pre-computed with a
successive order of scattering (SOS) code (Deuzé et al., 1989) for seven
aerosol models that follow a single lognormal size distribution. Six models
correspond to spherical aerosols (fine-mode particles) with radius from 0.06
to 0.16 <inline-formula><mml:math id="M18" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m, for which a complex refractive index of <inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.47</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:math></inline-formula> is
assumed. The seventh model is bimodal and characteristic of non-spherical
aerosols (dust) with a refractive index of <inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.47</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0007</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:math></inline-formula>. In the search for
the best-fitting aerosol model, the operational algorithm follows the
strategy described by Waquet et al. (2013b). After a first step, the
algorithm produces an approximation of the AOT at 865 nm. As a function of
this AOT value, a decision tree is applied: if the AOT is larger than 0.1
then the algorithm will search the best-fitting model within all the seven
models without any angular constraint for the selection of the POLDER data
(scattering angle ranging from 0 to 180<inline-formula><mml:math id="M21" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>). Next, if the mineral dust
model fails to reproduce the data or if the AOT retrieved in the first step
is smaller than 0.1, then only fine-mode models are considered in the
retrieval scheme and the viewing geometries are restricted to side or forward
viewing geometries (scattering angles smaller than 130<inline-formula><mml:math id="M22" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>). The AOT
threshold of 0.1 at 865 nm is empirical and was introduced since the
retrieval of the aerosol type (dust or fine-mode particles) becomes difficult
for small AOT.</p>
      <p>Collocated cloud properties retrieved from MODIS at high resolution (<inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> km<inline-formula><mml:math id="M24" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> at nadir) are
used to characterize and to select the cloudy scenes within a POLDER pixel
(6 km <inline-formula><mml:math id="M25" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 6 km at nadir). We only consider fully covered cloudy
pixels associated with optically thick liquid water clouds: the COT retrieved by MODIS has to be larger than 3 and a cloud phase
algorithm is applied to select liquid water clouds (Riedi et al., 2010).
Moreover, Waquet et al. (2013b) have introduced a mask to eliminate cirrus
above liquid clouds that makes use of the MODIS brightness temperature
difference (BTD) between 8.5 and 11 <inline-formula><mml:math id="M26" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m wavelength bands as well as
MODIS and POLDER cloud top pressure estimates. Lastly, the AOT retrievals at
the 6 km <inline-formula><mml:math id="M27" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 6 km spatial resolution are aggregated to
18 km <inline-formula><mml:math id="M28" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 18 km spatial grid. The retrieved solution is kept if the
number of 6 km <inline-formula><mml:math id="M29" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 6 km pixels is larger than 5 and if the standard
deviation computed for the mean AOT is smaller than 0.1. This latter
procedure allows to remove edges of clouds. In our study, we use the version
3.00 of the official output product PARASOL_PM02-L2 for AAC scenes available
at ICARE website (<uri>http://www.icare.univ-lille1.fr/parasol/products/).</uri></p>
</sec>
<sec id="Ch1.S2.SS2">
  <title>CALIOP methods</title>
<sec id="Ch1.S2.SS2.SSS1">
  <title>Operational method</title>
      <p>The CALIPSO lidar (CALIOP) is a frequency-doubled Nd:YAG laser,
dual-wavelength, dual-polarization, elastic backscatter lidar (Winker et al.,
2009). The lidar returned signal is normalized and range-corrected to provide
the total attenuated backscatter coefficient (km<inline-formula><mml:math id="M30" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> sr<inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p>In order to retrieve the attenuated backscatter data and the columnar AOT at
532 and 1064 nm, the operational CALIOP algorithm combines the feature and
layer detection scheme (Vaughan et al., 2009) with the extinction retrieval
algorithm (Young and Vaughan, 2009) that employs assumptions on the
extinction-to-backscatter ratio of aerosols. There are several steps involved
in the operational data processing: (1) cloud and aerosol layers are detected
in the backscattered signal along with their altitudes; (2) the algorithm
determines which layers have cloud or aerosol features; (3) the cloud
ice-water phase is estimated and the aerosol lidar ratio is determined, using
assumptions on the aerosol models; and finally (4) the extinction
coefficients and AOT are retrieved at 532 and 1064 nm.</p>
      <p>Lidar systems have a limited capability to determine the composition and size
of aerosols. Hypotheses are then used on the aerosol phase function at
180<inline-formula><mml:math id="M32" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and on the aerosol SSA in order to
calculate the aerosol lidar ratio. In the operational algorithm, the aerosol
models consist in a mixture of aerosol components characteristic of a region
or an air mass. It should be noted that an incorrect assumption for the lidar
ratio could be a source of substantial errors in the AOT retrieved with this
method.</p>
      <p>For our study we use the level 2 version 3.01 of the inversion products,
officially named CAL_LID_L2_05kmALay (ALay) and CAL_LID_L2_05kmCLay
(CLay) (which can be found at
<uri>http://www.icare.univ-lille1.fr/calipso/products/</uri>), which provide,
respectively, the aerosol and cloud layer parameters at a nominal horizontal
resolution of 5 km. From these products we used the AOTs retrieved at 532
and 1064 nm, the aerosol base and top altitudes, the cloud top altitude, the
ice-water cloud phase and the feature type. We also use CALIOP level 1
dataset, labelled CAL_LID_L1-ValStage1 (link above), which provides the
attenuated backscatter coefficient calculated at a vertical resolution of
30 m from <inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> to 8.2 km
altitude
and at 333 m horizontal resolution (Winker et al., 2007).</p>
</sec>
<sec id="Ch1.S2.SS2.SSS2">
  <title>Depolarization ratio method</title>
      <p>For retrieving the optical thickness of a thin high layer (aerosols or
clouds) above a lower and optically thick water cloud layer, Hu et
al. (2007a) and Chand et al. (2008) describe the depolarization ratio method
applied to CALIOP measurements. An opaque cloud with a minimum optical depth
of 3 will attenuate the lidar beam completely. For optically thick
clouds, we estimate the optical thickness of the above thin aerosol or cloud
layer by treating the opaque cloud as a target and by using the Beer–Lambert
law to estimate the direct transmission of light above this cloud layer. We
will refer to this product hereafter as DRM<inline-formula><mml:math id="M34" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula>.</p>
      <p>The physical properties used in this method are the cloud attenuated
backscatter coefficient (<inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mtext>water</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> integrated from the base
to the top of the cloud layer at 532 nm and the integrated attenuated
depolarization ratio (<inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> at 532 nm. When Rayleigh scattering
contribution has been corrected for, the definition of
<inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mi mathvariant="normal">water</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is given by the following equation:
              <disp-formula id="Ch1.E1" content-type="numbered"><mml:math id="M38" display="block"><mml:mrow><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">∫</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mi mathvariant="italic">_</mml:mi><mml:mtext>top</mml:mtext></mml:mrow><mml:mrow><mml:mi>z</mml:mi><mml:mi mathvariant="italic">_</mml:mi><mml:mtext>base</mml:mtext></mml:mrow></mml:munderover><mml:msup><mml:mi mathvariant="italic">β</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mtext>d</mml:mtext><mml:mi>z</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">β</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> is the total attenuated backscatter coefficient
(km<inline-formula><mml:math id="M40" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> sr<inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p>In situations where the cloud is optically thick and there are no aerosols
above the cloud, the lidar equation simplifies to the following definition,
expressed as a function of the lidar ratio (<inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and layer-effective multiple scattering factor (<inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (Platt, 1979):
              <disp-formula id="Ch1.E2" content-type="numbered"><mml:math id="M44" display="block"><mml:mrow><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mi mathvariant="normal">water</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">calc</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">∫</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mi mathvariant="italic">_</mml:mi><mml:mtext>top</mml:mtext></mml:mrow><mml:mrow><mml:mi>z</mml:mi><mml:mi mathvariant="italic">_</mml:mi><mml:mi mathvariant="normal">base</mml:mi></mml:mrow></mml:munderover><mml:msup><mml:mi mathvariant="italic">β</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mi mathvariant="normal">d</mml:mi><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mfenced open="(" close=")"><mml:mn mathvariant="normal">2</mml:mn><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
            <inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is narrowly constrained to about 19 sr at a wavelength of
532 nm. This value is typically used for liquid water clouds with droplets
smaller than about 50 <inline-formula><mml:math id="M46" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m (O'Connor et al., 2004; Pinnick et al.,
1983). <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, which takes a value between 0 and 1, is strongly
related to the cloud depolarization ratio <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> (defined as the ratio of
the parallel and perpendicular polarization signals), since multiple
scattering processes tend to depolarize light. An approximate relation was
derived from Monte Carlo simulations (Hu et al., 2006):
              <disp-formula id="Ch1.E3" content-type="numbered"><mml:math id="M49" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
            After <inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mi mathvariant="normal">water</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is corrected for molecular and gaseous
attenuation, the ratio between <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mi mathvariant="normal">water</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mi mathvariant="normal">water</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">calc</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> should be equal to 1 in the absence of higher
aerosol or cloud layer and have an accurate lidar calibration. Instead, in
case of an overlying aerosol or cloud layer, this ratio can be written as
              <disp-formula id="Ch1.E4" content-type="numbered"><mml:math id="M53" display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mi mathvariant="normal">water</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mi mathvariant="normal">water</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">calc</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:msup><mml:mi>T</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mi>exp⁡</mml:mi><mml:mfenced close=")" open="("><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="normal">top</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">DR</mml:mi></mml:mrow></mml:msub></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msup><mml:mi>T</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> is the transmission of light after a two-way propagation
between the sensor and the targeted cloud, and <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="normal">top</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">DR</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the
higher layer's optical thickness. It follows from Eq. (4) that the optical
depth (<inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="normal">top</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">DR</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is given by
              <disp-formula id="Ch1.E5" content-type="numbered"><mml:math id="M57" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="normal">top</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">DR</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mi>ln⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mn mathvariant="normal">2</mml:mn><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
            DRM<inline-formula><mml:math id="M58" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> differs from the operational method by the fact that it
does not rely on assumptions related to aerosol microphysical properties
(aerosol phase function and SSA) and does not require accurate layer
detection for the overlying aerosol layer in order to estimate the AOT
integrated over the atmospheric column. The main uncertainties of the
DRM<inline-formula><mml:math id="M59" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> are linked to the calibration of the lidar, which impact
the estimate of the parameters in Eq. (5).</p>
      <p>Providing a robust, self-calibrated method at global scale and for the whole
CALIPSO dataset is not trivial and, in order to improve the estimate of the
AOT with the DR method, the developers of the Synergized Optical Depth of
Aerosols and ICE clouds (SODA &amp; ICE, available at the ICARE thematic
centre), Josset et al. (2010, 2012), modified the original formalism of
DRM<inline-formula><mml:math id="M60" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula>. The main reason for these modifications is that the
relationship between the multiple scattering factor and the depolarization by
the cloud shows a systematic deviation from the theory (see Fig. 2 in Hu,
2007). The multiple scattering–depolarization relationship has been
confirmed by laboratory experiments (Cao et al., 2009). Even if it has to be
modified in the presence of submicrometer or non-spherical particles, the origin
of the discrepancy between theory and observation points towards an
instrumental issue. The long transient response of the receiver has been
proposed as an explanation and a correction was also proposed (Hu et al.,
2007b). There are, however, other issues related to the calibration of the
polarization channel that could explain the discrepancy. The low gain–high
gain merging scheme and the day–night calibration transfer are a significant
source of uncertainty. Previous research (Sassen and Zhu, 2009) found a bias
in the linear depolarization of cirrus clouds of around 30 %.</p>
      <p>In order to overcome these difficulties and improve the accuracy of the
method, SODA takes advantage of the high number of CALIOP observations of
liquid water clouds in the absence of AAC. Practically, the SODA algorithm
introduces global-scale correction factors in the multiple scattering
coefficient to depolarization relationship and a recalibrated value of the
liquid water cloud lidar ratio as a function of latitudes. These two
corrections come from the fact that, when the liquid water clouds are
optically dense and in absence of AAC, the lidar equation can be reduced to
Eq. (2). Over the ocean, the lidar ratio of most liquid water clouds is
relatively constant (Hu et al., 2006) and the multiple scattering coefficient
can be measured directly if the lidar is well calibrated. This correction
follows the original intent of DRM<inline-formula><mml:math id="M61" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> (Hu et al., 2007a), which
has always been to be a self-calibrated method, unaffected by instrumental or
geophysical uncertainties (see Eq. 4 of Hu et al., 2007a, and related
discussion). However, because the discrepancy between theory and observations
is due to an instrumental artefact linked to the receiver electronics, SODA
introduces a clearer separation between the parallel and perpendicular
channel than in DRM<inline-formula><mml:math id="M62" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> (Hu et al., 2007b). DRM<inline-formula><mml:math id="M63" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula>
relates the total backscatter coefficient to the ratio of perpendicular and
parallel backscatter coefficient while SODA links the parallel backscatter
coefficient to this ratio. This approach is supported by the theory of light
propagation in dense medium where the contribution of multiple scattering to
the perpendicular and parallel channel is identical (Xu and Alfano, 2005) and
by the analysis of CALIOP data.</p>
      <p>A preliminary and mandatory step of the calibration procedure is to select
optically opaque liquid water clouds with no AAC. The calibration modules of
SODA use the following criteria. Note that there is some level of redundancy
in order to increase data quality selection.
<list list-type="custom"><list-item><label>a.</label><p>Criteria of optical density:
<list list-type="bullet"><list-item><p>The top and bottom of the cloud is given by the 333 m CALIPSO cloud
product. This ensures a minimum level of signal strength and the presence of
a transparent atmosphere above it. Note that SODA corrects the molecular
attenuation above the cloud but does not contain an explicit correction of
it within the cloud because of the high scattering ratio of liquid water
clouds. Nonetheless, the molecular contribution is statistically taken into
account by the calibration procedure.</p></list-item><list-item><p>The maximum of the lidar signal is above the base of the cloud. This
ensures an adequate level of attenuation of the surface return.</p></list-item><list-item><p>The ocean surface integrated attenuated backscatter is below a
detectability threshold of <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:mn mathvariant="normal">7.5</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> sr<inline-formula><mml:math id="M65" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for nighttime data
and <inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> sr<inline-formula><mml:math id="M67" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for daytime data. This corresponds to a
COT of around 2 during daytime and 4–5 during nighttime,
which is when this filter is the most useful. The intent of this threshold is
the same as the previous criteria. More specifically, the goal is to use a
threshold such that half the shots are below the noise sensitivity of the
instrument.</p></list-item></list></p></list-item><list-item><label>b.</label><p>Criteria of cloud in liquid phase:
<list list-type="bullet"><list-item><p>The temperature at the top of the cloud is higher than 0 <inline-formula><mml:math id="M68" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. The
isotherm is defined by the GMAO (Global Modelling and Assimilation Office)
temperature when interpolated on the CALIPSO vertical grid.</p></list-item><list-item><p>The total cloud liquid water contained in a vertical column of atmosphere
retrieved from collocated pixels of AMSR-E/AMSR2 is larger than 0 mm.</p></list-item></list></p></list-item><list-item><label>c.</label><p>Criteria of clear air above the cloud:
<list list-type="bullet"><list-item><p>The total 532 nm integrated attenuated backscatter coefficient from 20 km
of altitude to the top of the cloud is below the following threshold:</p><p><disp-formula id="Ch1.E6" content-type="numbered"><mml:math id="M69" display="block"><mml:mrow><mml:munderover><mml:mo movablelimits="false">∫</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mi mathvariant="italic">_</mml:mi><mml:mi mathvariant="normal">top</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">20</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:munderover><mml:msup><mml:mi mathvariant="italic">β</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mtext>d</mml:mtext><mml:mi>z</mml:mi><mml:mo>&lt;</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>exp⁡</mml:mi><mml:mo>(</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="normal">air</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">mol</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">8</mml:mn><mml:mi mathvariant="italic">π</mml:mi></mml:mrow><mml:mn mathvariant="normal">3</mml:mn></mml:mfrac></mml:mstyle><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula></p><p>where <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="normal">air</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">mol</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the optical depth due to air Rayleigh
scattering and ozone absorption. The factor of 1.5 allows the reduction of
occurrences of false positives due to noise. It also allows us to simplify the
formalism as the King factor (Bates, 1984; King, 1923) can be neglected with
no expected impact on the results. As this filter introduces more aerosol
contamination during daytime (similar to Josset et al., 2010, Fig. 4), it
could be desirable to consider the shot-to-shot CALIOP cloud mask for future
version of the algorithm as SODA already uses this information for the scene
classification flag.</p></list-item></list></p></list-item></list></p>
      <p>As previously mentioned, even if the multiple scattering–depolarization
relationship has been confirmed by laboratory experiments (Cao et al., 2009),
the relationship between the multiple scattering factor and the
depolarization by the cloud shows a systematic deviation from the theory. It
has to be corrected, as it would introduce a bias in aerosol optical depth
with the particularly undesirable trait to correlate with cloud microphysical
properties. As a first step, SODA calibrates the multiple scattering to
depolarization relationship for nighttime data on a monthly basis. The data
of interest are based on Eq. (2) and can be written as
              <disp-formula id="Ch1.E7" content-type="numbered"><mml:math id="M71" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">geo</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">19</mml:mn><mml:mo>×</mml:mo><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mi mathvariant="normal">water</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">parallel</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mi mathvariant="normal">water</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">parallel</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the parallel-integrated
backscatter coefficient. This equation provides a direct measurement of the
multiple scattering coefficient of liquid water clouds (<inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">geo</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
when their lidar ratio is constant. The constant value of 19 sr used in the
SODA algorithm is based on Hu et al. (2006), who found a lidar ratio equal to
19.1 <inline-formula><mml:math id="M74" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.21 sr when the 41 droplet size distributions of Miles et
al. (2000) are used as inputs of a Mie scattering code.</p>
      <p>For all opaque liquid water clouds defined with the above criteria, SODA then
compares the direct measurement of the multiple scattering coefficient
(<inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">geo</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and the theory (<inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to find the second-order polynomial that best fit the data in the least-squares fit sense. This
defines the calibrated multiple scattering coefficient
(<inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">calibr</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>:

                  <disp-formula id="Ch1.E8" content-type="numbered"><mml:math id="M78" display="block"><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">calibr</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="normal">fit</mml:mi><mml:mfenced open="[" close="]"><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">geo</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mfenced></mml:mfenced><mml:mo>=</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>A</mml:mi><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi>B</mml:mi><mml:msubsup><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p>This procedure allows us to use a relationship between depolarization and
multiple scattering that fits the observation. Using Eq. (3) instead of
Eq. (8) would create an aerosol optical depth bias that would typically range
between 0.02 and 0.08. Although this is not always significant, this
correction is necessary as the resulting
ACAOT bias
does correlate with the cloud's microphysical properties. This is
particularly undesirable as the link between aerosol and cloud microphysical
properties is an active topic of research.</p>
      <p>As a second step, SODA calculates the apparent lidar ratio <inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">lat</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>
of all opaque liquid water clouds as a function of each degree of latitude
and for both 532 and 1064 nm. This procedure is done separately for daytime
and nighttime data. The latitudinal dependency  aims to correct the
calibration inaccuracies of CALIOP, which are dependent on latitude (Powell
et al., 2010) and possible geophysical variations of cloud microphysical
properties between the northern and southern hemispheres.
              <disp-formula id="Ch1.E9" content-type="numbered"><mml:math id="M80" display="block"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">lat</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">calibr</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mi mathvariant="normal">water</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">parallel</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></disp-formula>
            For the 4.5 years of data we considered in this study, the median
of <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">lat</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> for the nighttime data is 19.36 sr, which is
interestingly close from the theoretical value determined by Hu et
al. (2006). For daytime data, <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">lat</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is systematically higher and
with a median of 20.64 sr. The systematic daytime–nighttime difference could
be geophysical. However, it is premature to reach such conclusion until all
nighttime–daytime differences in the CALIPSO data have been addressed.</p>
      <p>Lastly, all these coefficients are finally integrated in the AOT retrieval
equation:
              <disp-formula id="Ch1.E10" content-type="numbered"><mml:math id="M83" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="normal">top</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">DRcalibr</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mi>ln⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mn mathvariant="normal">2</mml:mn><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">lat</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">calibr</mml:mi></mml:msub><mml:msub><mml:msup><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mi mathvariant="normal">water</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">parallel</mml:mi></mml:mrow></mml:msub></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p>Throughout this study, we will refer to this product as DRM<inline-formula><mml:math id="M84" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>,
which
can be found at ICARE  Data and Services Center
(<uri>http://www.icare.univ-lille1.fr/projects/soda</uri>/).</p>
</sec>
</sec>
<sec id="Ch1.S2.SS3">
  <title>Data selection</title>
<sec id="Ch1.S2.SS3.SSS1">
  <title>Collocation</title>
      <p>The A-Train satellites pass through close orbits within several minutes,
providing coincident observations of POLDER, MODIS and CALIOP instruments.
Using the nearest pixel approximation, CALIOP files are used as a space
reference for sampling POLDER and MODIS products. CALTRACK is the output
dataset and can be found at ICARE. It contains
coincident data from POLDER at 18 km <inline-formula><mml:math id="M85" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 18 km and MODIS, extracted
under the CALIOP track at 5 km horizontal resolution. The DRM<inline-formula><mml:math id="M86" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula>
and DRM<inline-formula><mml:math id="M87" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> optical depth retrievals are processed at the CALIOP
native resolution of 333 m and aggregated afterwards at 5 km horizontal
resolution. Moreover, for a better consistency of the AOT comparison, the
POLDER AOT was extrapolated at 532 nm using the AE retrieved with the POLDER
algorithm.</p>
      <p>We also limited the cloud top altitude at 5 km because we are interested in
low-level clouds. Likewise, we eliminated from our data analysis all
situations in which the aerosol top altitude exceeds 10 km. This maximal
value should be sufficient, since most of the biomass-burning and dust
aerosol layers are typically observed between 0.5 and 4.0 km over ocean
(Torres et al., 2013).</p>
</sec>
<sec id="Ch1.S2.SS3.SSS2">
  <title>Distinction between vertical profiles</title>
      <p>Additionally, we have employed an approach that is similar to the concept of
Costantino and Bréon (2013) to classify the type of AAC scenes. The
respective positions of the aerosol and cloud layers are defined using the
CALIOP ALay and CLay products. We classify the AAC scenes into three
categories: “attached”, “detached” and “undetermined”. The so-called
“attached cases” correspond to situations where the aerosol layer touches
the top of the beneath cloud layer. For these cases, we assume that the
vertical distance of the aerosol bottom altitude from cloud top altitude must
be lower than 100 m, without penetrating the cloud layer for more than
50 m. Inversely, the “detached cases” correspond to aerosol and cloud
layers that are considered well separated, considering a distance higher than
500 m between the aerosol base altitude and the cloud top. Aerosol layers
with the base altitude within a distance between 100 and 500 m above the
cloud layer are considered too uncertain and are excluded from our study. We
also removed the situations for which the detected CALIOP aerosol top and/or
bottom altitudes are located below the cloud top, assuming that these data
are highly uncertain. Practically, we rejected the CALIOP data for which the
aerosol layer penetrates the cloud layer by more than 50 m. The third
category, “undetermined”, corresponds to situations for which the respective
position of the aerosol or cloud layer is not identified by the CALIOP layer
detection algorithm (i.e. missing data), even though POLDER and DRM AAC AOT
retrievals are valid. We chose to keep these data in our analysis as they
cover the majority of POLDER AAC detected cases with a non-negligible AOT
(even if CALIOP classifies them as invalid or noise), as the purpose of the
paper is to better understand the differences between the methods.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><caption><p>The first row of the panel shows the lidar CALIOP attenuated
backscatter coefficients at 532 nm (km<inline-formula><mml:math id="M88" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> sr<inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and the second row
presents the CALIOP attenuated backscatter coefficients at 1064 nm for three
case studies: African biomass-burning aerosols (BBA)
above clouds on 13 August 2006 <bold>(a–d)</bold>, Saharan dust (DDA) on 4
August 2008 <bold>(e–h)</bold> and Siberian biomass-burning aerosols over the
Okhotsk Sea on 3 July 2008 <bold>(i–l)</bold>. For these cases, the above-cloud
AOT at 532 nm and the Ångström exponent (AE) as a function of
latitude, measured with several techniques, are displayed.</p></caption>
            <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://amt.copernicus.org/articles/10/3499/2017/amt-10-3499-2017-f01.png"/>

          </fig>

      <p>We also distinguish the “two-layer situation” (i.e. one aerosol layer and
one cloud layer) from the “multiple-layer situations” (more than one
aerosol layer and/or more than one cloud layer). These latter situations are
filtered in our analysis for the sake of simplicity (see Sects. 3.4 and 4).</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S3">
  <title>Regional analysis and case studies</title>
      <p>The results presented in this section were acquired from May to October 2008.
We selected three distinctive regions (see Fig. 2) that are under the
influence of various aerosol species and different types of clouds: (a) an
area that extends from 30<inline-formula><mml:math id="M90" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S to 5<inline-formula><mml:math id="M91" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N and 12<inline-formula><mml:math id="M92" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W to
14<inline-formula><mml:math id="M93" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E over the South Atlantic Ocean (SAO), (b) an area between 10
and 35<inline-formula><mml:math id="M94" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N and 10 and 40<inline-formula><mml:math id="M95" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W over the North Atlantic Ocean
(NAO) and (c) an area located between 35 and 60<inline-formula><mml:math id="M96" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N and 140 and
170<inline-formula><mml:math id="M97" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E over the North Pacific Ocean (NPO). The south of the African
continent is the main contributor to biomass-burning aerosols above clouds,
originating from manmade crops fires (Waquet et al., 2013b). These aerosols
are highly absorbing (SSA of approximately 0.84 at 865 nm) and associated
with high AE values; they mainly contribute to the fine mode. The NAO area is
mainly under the influence of dust aerosols originating from the Sahara for the time period of interest. These particles are mainly
non-spherical and contribute primary to the coarse mode. They are moderately
absorbing at the wavelength of CALIOP (532 nm) and almost non-absorbing at
865 nm (SSA of approximately 0.98) (Balkanski et al., 2007; Dubovik et al.,
2002; Peers et al., 2015). The NPO is associated with
various types of particles: fine-mode aerosols with rather scattering
properties originating from manmade pollution (Waquet et al., 2013a; Yu et
al., 2008), biomass burning from forest fires (Peers et al., 2015; Zhang et
al., 2003) and dust originated from the Asian deserts. Potential mixture of
these different species is also possible for this area (Yu et al., 2006).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><caption><p>Linear regressions of AOT calculated between different methods for
three case studies: African biomass-burning aerosols (BBA), Saharan dust
aerosols (DDA) and Siberian BBA. <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> represents the coefficient of determination (COD)
between the two sets of data.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row>  
         <oasis:entry namest="col1" nameend="col2">Linear regressions </oasis:entry>  
         <oasis:entry colname="col3">African BBA</oasis:entry>  
         <oasis:entry colname="col4">Saharan DDA</oasis:entry>  
         <oasis:entry colname="col5">Siberian BBA</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"/>  
         <oasis:entry colname="col3">(13 Aug 2006)</oasis:entry>  
         <oasis:entry colname="col4">(4 Aug 2008)</oasis:entry>  
         <oasis:entry colname="col5">(3 Jul 2008)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">DRM<inline-formula><mml:math id="M99" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> vs. POLDER</oasis:entry>  
         <oasis:entry colname="col2">Slope</oasis:entry>  
         <oasis:entry colname="col3">0.89 <inline-formula><mml:math id="M100" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>  
         <oasis:entry colname="col4">0.74 <inline-formula><mml:math id="M101" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.04</oasis:entry>  
         <oasis:entry colname="col5">0.56 <inline-formula><mml:math id="M102" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Intercept</oasis:entry>  
         <oasis:entry colname="col3">0.04 <inline-formula><mml:math id="M103" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>  
         <oasis:entry colname="col4">0.01 <inline-formula><mml:math id="M104" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02</oasis:entry>  
         <oasis:entry colname="col5">0.07 <inline-formula><mml:math id="M105" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.009</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"><inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (COD)</oasis:entry>  
         <oasis:entry colname="col3">0.93</oasis:entry>  
         <oasis:entry colname="col4">0.79</oasis:entry>  
         <oasis:entry colname="col5">0.90</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">DRM<inline-formula><mml:math id="M107" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> vs. POLDER</oasis:entry>  
         <oasis:entry colname="col2">Slope</oasis:entry>  
         <oasis:entry colname="col3">0.91 <inline-formula><mml:math id="M108" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>  
         <oasis:entry colname="col4">0.74 <inline-formula><mml:math id="M109" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.03</oasis:entry>  
         <oasis:entry colname="col5">0.60 <inline-formula><mml:math id="M110" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Intercept</oasis:entry>  
         <oasis:entry colname="col3">0.11 <inline-formula><mml:math id="M111" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>  
         <oasis:entry colname="col4">0.15 <inline-formula><mml:math id="M112" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02</oasis:entry>  
         <oasis:entry colname="col5">0.23 <inline-formula><mml:math id="M113" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.009</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"><inline-formula><mml:math id="M114" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (COD)</oasis:entry>  
         <oasis:entry colname="col3">0.93</oasis:entry>  
         <oasis:entry colname="col4">0.82</oasis:entry>  
         <oasis:entry colname="col5">0.89</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">CALIOP<inline-formula><mml:math id="M115" display="inline"><mml:msub><mml:mi/><mml:mtext>OM</mml:mtext></mml:msub></mml:math></inline-formula> vs. POLDER</oasis:entry>  
         <oasis:entry colname="col2">Slope</oasis:entry>  
         <oasis:entry colname="col3">0.19 <inline-formula><mml:math id="M116" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>  
         <oasis:entry colname="col4">0.86 <inline-formula><mml:math id="M117" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.11</oasis:entry>  
         <oasis:entry colname="col5">0.47 <inline-formula><mml:math id="M118" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.08</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Intercept</oasis:entry>  
         <oasis:entry colname="col3">0.05 <inline-formula><mml:math id="M119" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.16</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M121" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.07</oasis:entry>  
         <oasis:entry colname="col5"><inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.04</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M123" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.08</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"><inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (COD)</oasis:entry>  
         <oasis:entry colname="col3">0.35</oasis:entry>  
         <oasis:entry colname="col4">0.41</oasis:entry>  
         <oasis:entry colname="col5">0.45</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p>Cloud types and their associated optical and microphysical properties are
expected to be different in these three regions (Warren et al., 1988).
Low-level stratocumulus clouds typically cover the SAO, with some occurrences
of cumulus and altostratus clouds. Cumulus, altostratus clouds and some
stratocumulus clouds generally cover the NAO. The cloud cover is generally
fractional over this part of the Atlantic Ocean. Stratocumulus clouds also
frequently cover the NPO. Higher altostratus and cumulus clouds are also
often observed over this area. Cirrus clouds can be frequently found at
mid-latitudes and also in the intertropical convergence zone, which includes
the NPO and the NAO regions.</p>
      <p>We studied 6 months of data over each region to observe the consistency
between different techniques for various types of aerosols. For this part of
the study, we mixed the two-layer and multiple-layer situations and
we analysed all the data, disregarding the position of the aerosol and cloud
layers. A case study was selected for each region in order to show the
spatial variability of the AOT at 532 nm retrieved along the CALIOP
transect. The first case is related to a biomass-burning event detected off
the coast of Namibia on 13 August 2006. The second event concerns Saharan
dust lifted above clouds westwards over the NAO on
4 August 2008, and the third case concerns Siberian biomass-burning aerosols
transported over the Okhotsk Sea on 3 July 2008.</p>
      <p>Figure 1 presents the backscatter profile at 532 nm and at 1064 nm
(km<inline-formula><mml:math id="M125" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> sr<inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of the lidar CALIOP for the three case studies, which
directly provides information on the aerosol and cloud vertical distribution.
In addition, the AOT and AE values measured by different techniques are
presented along the CALIOP track. Additional results for the study cases
comparison are shown in Table 1.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><caption><p>The map presents the latitudinal and longitudinal boundaries of the
three regions used in the regional study (Sect. 3): South Atlantic Ocean
(SAO) extends from 30<inline-formula><mml:math id="M127" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S to 5<inline-formula><mml:math id="M128" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N and 12<inline-formula><mml:math id="M129" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W to
14<inline-formula><mml:math id="M130" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E, North Atlantic Ocean (NAO) is situated between 10 and
35<inline-formula><mml:math id="M131" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N and 10 and 40<inline-formula><mml:math id="M132" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W and North Pacific Ocean (NPO) is
located between 35 and 60<inline-formula><mml:math id="M133" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N and 140 and 170<inline-formula><mml:math id="M134" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E.</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://amt.copernicus.org/articles/10/3499/2017/amt-10-3499-2017-f02.pdf"/>

      </fig>

      <p>Figure 3 shows the regional comparison between the AOT and AE retrieved with
POLDER and DRM<inline-formula><mml:math id="M135" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> for a period of 6 months in 2008. The
retrieval of aerosol type becomes difficult at small AOT. Therefore the AE
comparison was performed only when the values of POLDER AOT at 865 nm and
DRM<inline-formula><mml:math id="M136" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT at 532 nm were larger than 0.1. The AE mean value is
shown with a dashed blue line. The lateral histograms show the data
distribution. For the AOT comparison the colour scale represents the POLDER
AE<inline-formula><mml:math id="M137" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">670</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">865</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>. In the case of AE comparison, the POLDER
AOT<inline-formula><mml:math id="M138" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> was also reported with a colour scale. The
above-mentioned description is also considered in Fig. 4, which presents the
regional comparison between the AOT and AE retrieved with POLDER and
CALIOP<inline-formula><mml:math id="M139" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> for the same period. Additional results for the regional
intercomparison are reported in Table 2.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F3" specific-use="star"><caption><p>The first row of the panel shows the comparison of AOT at 532 nm
retrieved from DRM<inline-formula><mml:math id="M140" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and POLDER methods, with the corresponding
POLDER AE colour scale, computed between 670 and 865 nm. The second row
presents the Ångström exponent comparison for AOTs larger than 0.1,
retrieved from DRM<inline-formula><mml:math id="M141" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and POLDER methods, with the corresponding
POLDER AOT at 532 nm colour scale. The measurements were made over a period
of 6 months (May to October 2008) and over three distinctive regions: South
Atlantic Ocean, between 30<inline-formula><mml:math id="M142" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S and 5<inline-formula><mml:math id="M143" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N and 12<inline-formula><mml:math id="M144" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W
and 14<inline-formula><mml:math id="M145" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E <bold>(a, b)</bold>; North Atlantic Ocean, between 10 and
35<inline-formula><mml:math id="M146" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N and 10 and 40<inline-formula><mml:math id="M147" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W <bold>(c, d)</bold>; and North Pacific
Ocean, between 35 and 60<inline-formula><mml:math id="M148" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N and 140 and
170<inline-formula><mml:math id="M149" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E <bold>(e, f)</bold>. The histograms present the data
distribution. The error bars in <bold>(a)</bold>, <bold>(c)</bold> and <bold>(e)</bold>
represent the standard error of the mean (SEM).</p></caption>
        <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://amt.copernicus.org/articles/10/3499/2017/amt-10-3499-2017-f03.png"/>

      </fig>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T2" specific-use="star"><caption><p>Linear regressions of AOT calculated between different methods for
data acquired over 6 months (May to October 2008), over three different
regions: South Atlantic Ocean (SAO), North Atlantic Ocean (NAO) and North
Pacific Ocean (NPO).</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry namest="col1" nameend="col2">Linear regressions </oasis:entry>  
         <oasis:entry colname="col3">SAO</oasis:entry>  
         <oasis:entry colname="col4">NAO</oasis:entry>  
         <oasis:entry colname="col5">NPO</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">DRM<inline-formula><mml:math id="M150" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> vs. POLDER</oasis:entry>  
         <oasis:entry colname="col2">Slope</oasis:entry>  
         <oasis:entry colname="col3">0.89 <inline-formula><mml:math id="M151" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.004</oasis:entry>  
         <oasis:entry colname="col4">0.81 <inline-formula><mml:math id="M152" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.009</oasis:entry>  
         <oasis:entry colname="col5">0.76 <inline-formula><mml:math id="M153" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Intercept</oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math id="M154" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.03 <inline-formula><mml:math id="M155" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.001</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math id="M156" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.09 <inline-formula><mml:math id="M157" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.004</oasis:entry>  
         <oasis:entry colname="col5"><inline-formula><mml:math id="M158" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.03 <inline-formula><mml:math id="M159" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.003</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"><inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (COD)</oasis:entry>  
         <oasis:entry colname="col3">0.83</oasis:entry>  
         <oasis:entry colname="col4">0.82</oasis:entry>  
         <oasis:entry colname="col5">0.37</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">DRM<inline-formula><mml:math id="M161" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> vs. POLDER</oasis:entry>  
         <oasis:entry colname="col2">Slope</oasis:entry>  
         <oasis:entry colname="col3">0.90 <inline-formula><mml:math id="M162" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.004</oasis:entry>  
         <oasis:entry colname="col4">0.86 <inline-formula><mml:math id="M163" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>  
         <oasis:entry colname="col5">0.76 <inline-formula><mml:math id="M164" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Intercept</oasis:entry>  
         <oasis:entry colname="col3">0.05 <inline-formula><mml:math id="M165" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.001</oasis:entry>  
         <oasis:entry colname="col4">0.04 <inline-formula><mml:math id="M166" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.004</oasis:entry>  
         <oasis:entry colname="col5">0.13 <inline-formula><mml:math id="M167" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.003</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"><inline-formula><mml:math id="M168" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (COD)</oasis:entry>  
         <oasis:entry colname="col3">0.82</oasis:entry>  
         <oasis:entry colname="col4">0.82</oasis:entry>  
         <oasis:entry colname="col5">0.44</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">CALIOP<inline-formula><mml:math id="M169" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> vs. POLDER</oasis:entry>  
         <oasis:entry colname="col2">Slope</oasis:entry>  
         <oasis:entry colname="col3">0.34 <inline-formula><mml:math id="M170" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.004</oasis:entry>  
         <oasis:entry colname="col4">0.52 <inline-formula><mml:math id="M171" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02</oasis:entry>  
         <oasis:entry colname="col5">0.28 <inline-formula><mml:math id="M172" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Intercept</oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math id="M173" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.04 <inline-formula><mml:math id="M174" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.002</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math id="M175" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.01 <inline-formula><mml:math id="M176" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>  
         <oasis:entry colname="col5">0.01 <inline-formula><mml:math id="M177" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"><inline-formula><mml:math id="M178" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (COD)</oasis:entry>  
         <oasis:entry colname="col3">0.43</oasis:entry>  
         <oasis:entry colname="col4">0.42</oasis:entry>  
         <oasis:entry colname="col5">0.24</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">CALIOP<inline-formula><mml:math id="M179" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> vs. DRM<inline-formula><mml:math id="M180" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Slope</oasis:entry>  
         <oasis:entry colname="col3">0.34 <inline-formula><mml:math id="M181" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.002</oasis:entry>  
         <oasis:entry colname="col4">0.62 <inline-formula><mml:math id="M182" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>  
         <oasis:entry colname="col5">0.35 <inline-formula><mml:math id="M183" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Intercept</oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math id="M184" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.01 <inline-formula><mml:math id="M185" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.002</oasis:entry>  
         <oasis:entry colname="col4">0.04 <inline-formula><mml:math id="M186" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.006</oasis:entry>  
         <oasis:entry colname="col5">0.01 <inline-formula><mml:math id="M187" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.007</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"><inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (COD)</oasis:entry>  
         <oasis:entry colname="col3">0.42</oasis:entry>  
         <oasis:entry colname="col4">0.48</oasis:entry>  
         <oasis:entry colname="col5">0.28</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><caption><p>Same as Fig. 3, retrieved from CALIOP operational method and POLDER
method.</p></caption>
        <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://amt.copernicus.org/articles/10/3499/2017/amt-10-3499-2017-f04.png"/>

      </fig>

<sec id="Ch1.S3.SS1">
  <title>African biomass-burning aerosols</title>
      <p>According to the CALIOP vertical profile at 532 nm of the biomass-burning
case (Fig. 1a), the cloud top is at around 1.5 km and the aerosol layer is
located between 3 and 5 km. The 1064 nm backscatter profile (Fig. 1b)
exhibits an aerosol layer with a larger vertical extent, showing  more
potential contact area with the underlying cloud. We observe a thin cirrus
cloud between 10 and 12<inline-formula><mml:math id="M189" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S that was not filtered, probably because the
cirrus is optically too thin (Fig. 1c and d). In general, there is an
excellent agreement between POLDER, DRM<inline-formula><mml:math id="M190" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> and DRM<inline-formula><mml:math id="M191" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>
AOT retrievals with a square correlation <inline-formula><mml:math id="M192" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.93 (see Table 1). High
values of AOT are retrieved by the different methods, with AOT values as
large as 1.5. The retrieved POLDER AE<inline-formula><mml:math id="M193" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">670</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">865</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is larger than 1.8
(Fig. 1d), which is characteristic of fine-mode particles (Dubovik et al.,
2002). The DRM<inline-formula><mml:math id="M194" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AE<inline-formula><mml:math id="M195" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">1064</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is consistent with the POLDER
AE, with values higher than 1.5. AOT values retrieved by CALIOP<inline-formula><mml:math id="M196" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula>
are much lower than the ones retrieved by the three other techniques. The
maximal AOT retrieved by CALIOP<inline-formula><mml:math id="M197" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> at 532 nm is 0.5. A possible
explanation for this potential low bias was proposed by Jethva et al. (2014):
in case of optically thick aerosol layer, the sensitivity of the
backscattered signal to the altitude of the base of the aerosol layer would
be reduced or lost, being strongly attenuated by the two-way transmission
term. As a result, the operational algorithm may overestimate the aerosol
base altitude and so underestimate the geometrical thickness of the aerosol
layer and consequently the AOT. The selection of an inappropriate aerosol
model (i.e. aerosol lidar ratio <inline-formula><mml:math id="M198" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for biomass burning varies
between 70 <inline-formula><mml:math id="M199" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 28 at 532 nm and 40 <inline-formula><mml:math id="M200" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 24 sr at 1064 nm; Cattrall
et al., 2005; Omar et al., 2005) or the significant biases found in the V3.01
CALIOP 1064 nm calibration might also contribute to the underestimation of
the AOT for this case study. The CALIOP<inline-formula><mml:math id="M201" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> mean AE<inline-formula><mml:math id="M202" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">1064</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>
seems quite low for fine-mode particles (AE values are lower than 1). The
selection of an inappropriate aerosol model might also contribute to the
underestimation of the AOT for this case study.</p>
      <p>Regional analysis shows that South Atlantic region is mostly characterized by
biomass-burning aerosols with large AOT and AE (Fig. 3a and b). On average,
the cloud top height is located below 1.5 km, while the aerosol layers are
frequently located between 2.5 and 4 km (see Table 3). The
AOT<inline-formula><mml:math id="M203" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> measured by DRM<inline-formula><mml:math id="M204" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and POLDER may reach
values as large as 1.30 (Fig. 3a), with 80 % of the retrieved AOTs
ranging between 0.05 and 0.8. This AOT intercomparison shows close
correlation between DRM<inline-formula><mml:math id="M205" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and POLDER (<inline-formula><mml:math id="M206" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.83). The
mean value of POLDER AE<inline-formula><mml:math id="M207" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">670</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">865</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is 2.05, whereas the mean
DRM<inline-formula><mml:math id="M208" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AE<inline-formula><mml:math id="M209" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">1064</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is 1.79 (Table 5) (both typical for BBA).
DRM<inline-formula><mml:math id="M210" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> and DRM<inline-formula><mml:math id="M211" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> give rather same results. From the
linear regressions performed (see Table 2) we can observe that the offset is
always positive for DRM<inline-formula><mml:math id="M212" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> and systematically larger than the
absolute value for DRM<inline-formula><mml:math id="M213" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> when compared to POLDER method. The
AOT estimated by POLDER is constantly between DRM<inline-formula><mml:math id="M214" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> and
DRM<inline-formula><mml:math id="M215" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>.</p>
      <p>We do not find a good correlation between the CALIOP<inline-formula><mml:math id="M216" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> and POLDER AOT
and AE retrievals. The CALIOP<inline-formula><mml:math id="M217" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> mean AOT<inline-formula><mml:math id="M218" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> is 0.12 and the mean
AE<inline-formula><mml:math id="M219" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">1064</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is 0.97. Comparing with POLDER and DRM<inline-formula><mml:math id="M220" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>,
CALIOP<inline-formula><mml:math id="M221" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> is underestimating the ACAOT by a factor of 2.92.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <title>Saharan  dust aerosols</title>
      <p>For the mineral dust case (Fig. 1e), the cloud top altitude is located at
approximately 1 km altitude whereas the aerosol layer is located between 2
and 5 km for latitudes between 18 and 23<inline-formula><mml:math id="M222" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N. Figure 1g shows that
the POLDER, DRM<inline-formula><mml:math id="M223" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and DRM<inline-formula><mml:math id="M224" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> AOT<inline-formula><mml:math id="M225" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula>
increase up to 0.92, following the same gradient. The correlation
coefficients between POLDER parameters and DRM<inline-formula><mml:math id="M226" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> and
DRM<inline-formula><mml:math id="M227" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> parameters are close (Table 1). The majority of POLDER
AE<inline-formula><mml:math id="M228" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">670</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">865</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and DRM<inline-formula><mml:math id="M229" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AE<inline-formula><mml:math id="M230" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">1064</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is associated with
values lower than 0.4 (Fig. 1h), which indicates that coarse-mode particles
are predominant (Dubovik et al., 2002). Except for few retrievals associated
with an abrupt change in the AE and AOT measured by CALIOP<inline-formula><mml:math id="M231" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula>
(around 21<inline-formula><mml:math id="M232" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N in latitude), 90 % of the CALIOP<inline-formula><mml:math id="M233" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula>
AOT<inline-formula><mml:math id="M234" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> is lower than 0.45, being once again underestimated
with respect to the other estimates. Most of CALIOP<inline-formula><mml:math id="M235" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula>
AE<inline-formula><mml:math id="M236" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">1064</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> values are underestimated (i.e. overestimation of the
particles size) in comparison with the AE retrieved by the two other
algorithms. These low values of AOT and AE may be explained once more by a
biased CALIOP calibration at 1064 nm combined with an unfitted model
selection (i.e. for desert dust, <inline-formula><mml:math id="M237" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is equal to 40 <inline-formula><mml:math id="M238" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 20 sr
at 532 nm and 55 <inline-formula><mml:math id="M239" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 17 sr at 1064 nm; Cattrall et al., 2005; Omar et
al., 2005).</p>
      <p>A regional study shows similar AOT and AE results over the North Atlantic
region (Fig. 3c). On average, the aerosol layers are located between 3 and
4.5 km and the cloud top heights are typically around 1.4 km (see Table 3).
The values of AOT<inline-formula><mml:math id="M240" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">532</mml:mn></mml:msub></mml:math></inline-formula> retrieved from POLDER and DRM<inline-formula><mml:math id="M241" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> are
well correlated (<inline-formula><mml:math id="M242" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.82), with maximum values of, respectively, 1.19
and 0.95. Nonetheless, we observe a larger offset between DRM<inline-formula><mml:math id="M243" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>
and POLDER AOT<inline-formula><mml:math id="M244" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> for this region (<inline-formula><mml:math id="M245" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.09</mml:mn></mml:mrow></mml:math></inline-formula>) compared to the
South Atlantic Ocean region (<inline-formula><mml:math id="M246" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.03</mml:mn></mml:mrow></mml:math></inline-formula>). The use of only one dust model in the
LUT algorithm used for POLDER remains a limitation that might explain this
larger offset. The introduction of additional dust models with larger or
smaller effective radius values may contribute to improve the AOT retrievals
for dust AAC events. Regarding the POLDER AE<inline-formula><mml:math id="M247" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">670</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">865</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> retrievals, most of
the values are lower than 0.4, which is expected for desert dust aerosols
(Fig. 3c and d). However, for AOT values lower than 0.2, the AE<inline-formula><mml:math id="M248" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">670</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">865</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>
retrieved by POLDER is between 1.4 and 2.2. This is explained by the fact
that the selection of the dust model is not permitted in the POLDER algorithm
in case of low AOTs. Nonetheless, all three methods are consistent in
revealing the predominance of the coarse mode. The mean values for the AE are
0.49 for POLDER, 0.10 for DRM<inline-formula><mml:math id="M249" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and <inline-formula><mml:math id="M250" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.19</mml:mn></mml:mrow></mml:math></inline-formula> for
CALIOP<inline-formula><mml:math id="M251" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula>. The AOT<inline-formula><mml:math id="M252" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> correlation between
CALIOP<inline-formula><mml:math id="M253" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> and POLDER is low, with <inline-formula><mml:math id="M254" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.42.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3"><caption><p>Regional analysis using CALIOP measurements over 6 months (May to
October 2008), over South Atlantic Ocean (SAO), North Atlantic Ocean (NAO)
and North Pacific Ocean (NPO): mean cloud altitude for altitudes smaller than
5 km, mean aerosol base and top altitudes for altitudes smaller than
10 km.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">SAO</oasis:entry>  
         <oasis:entry colname="col3">NAO</oasis:entry>  
         <oasis:entry colname="col4">NPO</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">Mean cloud top</oasis:entry>  
         <oasis:entry colname="col2">1.24 <inline-formula><mml:math id="M255" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.43</oasis:entry>  
         <oasis:entry colname="col3">1.35 <inline-formula><mml:math id="M256" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.5</oasis:entry>  
         <oasis:entry colname="col4">1.09 <inline-formula><mml:math id="M257" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.84</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">altitude (km)</oasis:entry>  
         <oasis:entry colname="col2">Min: 0.30</oasis:entry>  
         <oasis:entry colname="col3">Min: 0.20</oasis:entry>  
         <oasis:entry colname="col4">Min: 0.05</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Max: 4.95</oasis:entry>  
         <oasis:entry colname="col3">Max: 3.25</oasis:entry>  
         <oasis:entry colname="col4">Max: 5.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Mean aerosol top</oasis:entry>  
         <oasis:entry colname="col2">3.83 <inline-formula><mml:math id="M258" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.093</oasis:entry>  
         <oasis:entry colname="col3">4.50 <inline-formula><mml:math id="M259" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.03</oasis:entry>  
         <oasis:entry colname="col4">2.74 <inline-formula><mml:math id="M260" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.68</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">altitude (km)</oasis:entry>  
         <oasis:entry colname="col2">Min: 0.50</oasis:entry>  
         <oasis:entry colname="col3">Min: 0.44</oasis:entry>  
         <oasis:entry colname="col4">Min: 0.47</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Max: 6.73</oasis:entry>  
         <oasis:entry colname="col3">Max: 6.67</oasis:entry>  
         <oasis:entry colname="col4">Max: 9.85</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Mean aerosol base</oasis:entry>  
         <oasis:entry colname="col2">2.90 <inline-formula><mml:math id="M261" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.97</oasis:entry>  
         <oasis:entry colname="col3">2.97 <inline-formula><mml:math id="M262" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.12</oasis:entry>  
         <oasis:entry colname="col4">3.48 <inline-formula><mml:math id="M263" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.78</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">altitude (km)</oasis:entry>  
         <oasis:entry colname="col2">Min: 0.02</oasis:entry>  
         <oasis:entry colname="col3">Min: 0.02</oasis:entry>  
         <oasis:entry colname="col4">Min: 0.05</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Max: 5.80</oasis:entry>  
         <oasis:entry colname="col3">Max: 5.74</oasis:entry>  
         <oasis:entry colname="col4">Max: 9.31</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T4"><caption><p>Calculated mean, minimum value and maximum value of
AOT<inline-formula><mml:math id="M264" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> over 6 months in 2008, for three regions (SAO, NAO,
NPO) and for different methods.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.95}[.95]?><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry namest="col1" nameend="col2">AOT<inline-formula><mml:math id="M265" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">SAO</oasis:entry>  
         <oasis:entry colname="col4">NAO</oasis:entry>  
         <oasis:entry colname="col5">NPO</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">POLDER</oasis:entry>  
         <oasis:entry colname="col2">Mean</oasis:entry>  
         <oasis:entry colname="col3">0.35 <inline-formula><mml:math id="M266" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.23</oasis:entry>  
         <oasis:entry colname="col4">0.39 <inline-formula><mml:math id="M267" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.21</oasis:entry>  
         <oasis:entry colname="col5">0.18 <inline-formula><mml:math id="M268" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.21</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Min</oasis:entry>  
         <oasis:entry colname="col3">0.005</oasis:entry>  
         <oasis:entry colname="col4">0.005</oasis:entry>  
         <oasis:entry colname="col5">0.005</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Max</oasis:entry>  
         <oasis:entry colname="col3">1.27</oasis:entry>  
         <oasis:entry colname="col4">1.19</oasis:entry>  
         <oasis:entry colname="col5">2.17</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">DRM<inline-formula><mml:math id="M269" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Mean</oasis:entry>  
         <oasis:entry colname="col3">0.28 <inline-formula><mml:math id="M270" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.22</oasis:entry>  
         <oasis:entry colname="col4">0.23 <inline-formula><mml:math id="M271" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.19</oasis:entry>  
         <oasis:entry colname="col5">0.15 <inline-formula><mml:math id="M272" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.38</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Min</oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math id="M273" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.13</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math id="M274" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.16</oasis:entry>  
         <oasis:entry colname="col5"><inline-formula><mml:math id="M275" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.16</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Max</oasis:entry>  
         <oasis:entry colname="col3">1.30</oasis:entry>  
         <oasis:entry colname="col4">0.95</oasis:entry>  
         <oasis:entry colname="col5">3.26</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">DRM<inline-formula><mml:math id="M276" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Mean</oasis:entry>  
         <oasis:entry colname="col3">0.37 <inline-formula><mml:math id="M277" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.23</oasis:entry>  
         <oasis:entry colname="col4">0.38 <inline-formula><mml:math id="M278" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.20</oasis:entry>  
         <oasis:entry colname="col5">0.32 <inline-formula><mml:math id="M279" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.40</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Min</oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math id="M280" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.07</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math id="M281" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.06</oasis:entry>  
         <oasis:entry colname="col5"><inline-formula><mml:math id="M282" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.06</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Max</oasis:entry>  
         <oasis:entry colname="col3">1.50</oasis:entry>  
         <oasis:entry colname="col4">1.17</oasis:entry>  
         <oasis:entry colname="col5">3.68</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">CALIOP<inline-formula><mml:math id="M283" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Mean</oasis:entry>  
         <oasis:entry colname="col3">0.12 <inline-formula><mml:math id="M284" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.11</oasis:entry>  
         <oasis:entry colname="col4">0.23 <inline-formula><mml:math id="M285" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.18</oasis:entry>  
         <oasis:entry colname="col5">0.14 <inline-formula><mml:math id="M286" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.23</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Min</oasis:entry>  
         <oasis:entry colname="col3">0.001</oasis:entry>  
         <oasis:entry colname="col4">0.005</oasis:entry>  
         <oasis:entry colname="col5">0.001</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Max</oasis:entry>  
         <oasis:entry colname="col3">1.88</oasis:entry>  
         <oasis:entry colname="col4">2.38</oasis:entry>  
         <oasis:entry colname="col5">2.01</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><caption><p>Global comparison over a period of 4.5 years
(June 2006–December 2010) for situations with aerosol layer well separated
from the cloud top (“detached”; <bold>a, b</bold>), for cases where the
aerosol layer is in contact with the cloud (“attached”; <bold>c, d</bold>) and for
“undetermined”
situations <bold>(e, f)</bold>. The comparison of AOT at 532 nm retrieved from
DRM<inline-formula><mml:math id="M287" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and POLDER methods is shown in the first row. The colour
scale represents the corresponding POLDER AE computed between 670 and
865 nm. The second row presents the Ångström exponent for AOTs
larger than 0.1, with a POLDER AOT at 532 nm colour scale. The histograms
present the data distribution. The error bars in <bold>(a)</bold>, <bold>(c)</bold>
and <bold>(e)</bold> represent the standard error of the mean (SEM).</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://amt.copernicus.org/articles/10/3499/2017/amt-10-3499-2017-f05.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS3">
  <title>East Asian mixture of aerosols</title>
      <p>The CALIOP transect shows that Siberian biomass-burning case is located
between 40 and 52<inline-formula><mml:math id="M288" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, the cloud top altitude is constantly around
1 km and the base of the aerosol layer decreases from 10 km in the south
(at 45<inline-formula><mml:math id="M289" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) to around 2 km in the north (at 54<inline-formula><mml:math id="M290" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N)
(Fig. 1i). We notice also cirrus clouds at high altitude (around 10 km)
between 47 and 51<inline-formula><mml:math id="M291" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, which were efficiently eliminated from the
retrievals (Fig. 1k). The maximum POLDER AOT value is as large as 1.9, while
DRM reaches 1.3 in AOT. Nonetheless, Table 1 shows that POLDER and DRM
methods AOT<inline-formula><mml:math id="M292" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> retrievals are consistent (<inline-formula><mml:math id="M293" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.90).
POLDER AE<inline-formula><mml:math id="M294" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">670</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">865</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> values are between 1.7 and 2.3, indicating small
particles of smoke, while DRM<inline-formula><mml:math id="M295" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AE<inline-formula><mml:math id="M296" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">1064</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> has a large
range of values (Fig. 1l). The number of sampled ACAOT events by
CALIOP<inline-formula><mml:math id="M297" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> is 4.5 times less than of POLDER and
DRM<inline-formula><mml:math id="M298" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>. For these, the CALIOP<inline-formula><mml:math id="M299" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> AOTs are
underestimated by a factor of 1.5 compared to ones retrieved by the other
methods. Also, the correlation coefficient with POLDER is 0.45.</p>
      <p>On a regional scale, this area is under the influence of various aerosols
(BBA, DDA, pollution) and elevated cirrus clouds are frequent. The mean cloud
top altitude is around 1 km and the aerosols are between 2.5 km and
4.0 km. As indicated in Table 3, the maximum aerosol altitude is 9.85 km,
which might suggests cirrus misclassification. In some cases,
DRM<inline-formula><mml:math id="M300" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> gives large values of AOT<inline-formula><mml:math id="M301" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> (larger than
1) whereas the POLDER estimates AOT<inline-formula><mml:math id="M302" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> smaller than 0.2.
These situations could be explained by a misinterpretation of thin cirrus
clouds as aerosols. Otherwise, the POLDER mean AOT<inline-formula><mml:math id="M303" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> and
DRM<inline-formula><mml:math id="M304" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT<inline-formula><mml:math id="M305" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> are in rather close agreement
(0.18 and 0.15, respectively; see Table 4), but the correlation between them
is low (<inline-formula><mml:math id="M306" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.37, Table 2). All methods show a large variability for
the retrieved AE, with values that correspond to particle size distributions
dominated by coarse or fine modes and mixtures (Table 5). As previously
mentioned, the algorithm developed for POLDER uses a bimodal aerosol model
for dust. However, the possibility of mixing different fine and coarse
aerosol models in various proportions is not yet included. This might explain
why we found a lower correlation between the POLDER and DRM retrievals for
this region. As for above, the CALIOP<inline-formula><mml:math id="M307" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> and POLDER
AOT<inline-formula><mml:math id="M308" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> are not correlated (<inline-formula><mml:math id="M309" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.24).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T5" specific-use="star"><caption><p>Mean value of AE over 6 months in 2008 for three regions (SAO,
NAO, NPO) for different methods after filtering the POLDER
AOT<inline-formula><mml:math id="M310" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">865</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> and DRM<inline-formula><mml:math id="M311" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT<inline-formula><mml:math id="M312" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> and the CALIOP<inline-formula><mml:math id="M313" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> AOT<inline-formula><mml:math id="M314" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula>.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry namest="col1" nameend="col2" align="center"/>  
         <oasis:entry colname="col3">SAO</oasis:entry>  
         <oasis:entry colname="col4">NAO</oasis:entry>  
         <oasis:entry colname="col5">NPO</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">POLDER</oasis:entry>  
         <oasis:entry colname="col2">Mean AE<inline-formula><mml:math id="M315" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">670</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">865</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">2.05 <inline-formula><mml:math id="M316" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.27</oasis:entry>  
         <oasis:entry colname="col4">0.49 <inline-formula><mml:math id="M317" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.27</oasis:entry>  
         <oasis:entry colname="col5">1.67 <inline-formula><mml:math id="M318" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.50</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Min</oasis:entry>  
         <oasis:entry colname="col3">0.36</oasis:entry>  
         <oasis:entry colname="col4">0.36</oasis:entry>  
         <oasis:entry colname="col5">0.36</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Max</oasis:entry>  
         <oasis:entry colname="col3">2.56</oasis:entry>  
         <oasis:entry colname="col4">2.03</oasis:entry>  
         <oasis:entry colname="col5">2.39</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">DRM<inline-formula><mml:math id="M319" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Mean AE<inline-formula><mml:math id="M320" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">1064</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">1.79 <inline-formula><mml:math id="M321" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.58</oasis:entry>  
         <oasis:entry colname="col4">0.10 <inline-formula><mml:math id="M322" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.27</oasis:entry>  
         <oasis:entry colname="col5">1.47 <inline-formula><mml:math id="M323" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.84</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Min</oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math id="M324" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.15</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math id="M325" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.14</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"><inline-formula><mml:math id="M326" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.21</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Max</oasis:entry>  
         <oasis:entry colname="col3">4.19</oasis:entry>  
         <oasis:entry colname="col4">1.43</oasis:entry>  
         <oasis:entry colname="col5">3.93</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">CALIOP<inline-formula><mml:math id="M327" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Mean AE<inline-formula><mml:math id="M328" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">1064</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">0.97 <inline-formula><mml:math id="M329" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.51</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math id="M330" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.19</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M331" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.32</oasis:entry>  
         <oasis:entry colname="col5">0.41 <inline-formula><mml:math id="M332" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.72</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Min</oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math id="M333" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2.27</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math id="M334" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.62</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"><inline-formula><mml:math id="M335" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2.63</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Max</oasis:entry>  
         <oasis:entry colname="col3">3.16</oasis:entry>  
         <oasis:entry colname="col4">1.27</oasis:entry>  
         <oasis:entry colname="col5">4.41</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T6" specific-use="star"><caption><p>Linear regression calculated between DRM<inline-formula><mml:math id="M336" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>
AOT<inline-formula><mml:math id="M337" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> and POLDER AOT<inline-formula><mml:math id="M338" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> for situations when
the aerosol layer is attached to the cloud top and when the aerosol layer is
well separated from the cloud over three regions (South Atlantic Ocean, North
Atlantic Ocean and North Pacific Ocean) and for a period of 4.5
years. </p></caption><oasis:table frame="topbot"><oasis:tgroup cols="7">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right" colsep="1"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right" colsep="1"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:thead>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry rowsep="1" namest="col2" nameend="col3" align="center" colsep="1">SAO </oasis:entry>  
         <oasis:entry rowsep="1" namest="col4" nameend="col5" align="center" colsep="1">NAO </oasis:entry>  
         <oasis:entry rowsep="1" namest="col6" nameend="col7" align="center">NPO </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Attached</oasis:entry>  
         <oasis:entry colname="col3">Detached</oasis:entry>  
         <oasis:entry colname="col4">Attached</oasis:entry>  
         <oasis:entry colname="col5">Detached</oasis:entry>  
         <oasis:entry colname="col6">Attached</oasis:entry>  
         <oasis:entry colname="col7">Detached</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">Slope</oasis:entry>  
         <oasis:entry colname="col2">0.60 <inline-formula><mml:math id="M339" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02</oasis:entry>  
         <oasis:entry colname="col3">0.77 <inline-formula><mml:math id="M340" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.003</oasis:entry>  
         <oasis:entry colname="col4">0.63 <inline-formula><mml:math id="M341" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.07</oasis:entry>  
         <oasis:entry colname="col5">0.59 <inline-formula><mml:math id="M342" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>  
         <oasis:entry colname="col6">0.78 <inline-formula><mml:math id="M343" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.12</oasis:entry>  
         <oasis:entry colname="col7">0.80 <inline-formula><mml:math id="M344" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Intercept</oasis:entry>  
         <oasis:entry colname="col2">0.04 <inline-formula><mml:math id="M345" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.006</oasis:entry>  
         <oasis:entry colname="col3">0.02 <inline-formula><mml:math id="M346" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.001</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math id="M347" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.005</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M348" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02</oasis:entry>  
         <oasis:entry colname="col5"><inline-formula><mml:math id="M349" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.011</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M350" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.006</oasis:entry>  
         <oasis:entry colname="col6"><inline-formula><mml:math id="M351" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.04</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M352" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02</oasis:entry>  
         <oasis:entry colname="col7"><inline-formula><mml:math id="M353" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.015</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M354" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.007</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math id="M355" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (COD)</oasis:entry>  
         <oasis:entry colname="col2">0.54</oasis:entry>  
         <oasis:entry colname="col3">0.715</oasis:entry>  
         <oasis:entry colname="col4">0.39</oasis:entry>  
         <oasis:entry colname="col5">0.57</oasis:entry>  
         <oasis:entry colname="col6">0.19</oasis:entry>  
         <oasis:entry colname="col7">0.435</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p>In general, there is a good agreement between POLDER and DRM<inline-formula><mml:math id="M356" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>
AOTs, especially when the fine mode or coarse mode dominates the particle
size distribution (i.e. BBA and DDA). Overall, DRM<inline-formula><mml:math id="M357" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and
DRM<inline-formula><mml:math id="M358" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> give similar results. However, the AOTs retrieved with
DRM<inline-formula><mml:math id="M359" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> are generally larger than those of DRM<inline-formula><mml:math id="M360" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> for
all the three regions (i.e. 0.37 compared to 0.28 for SAO; see Table 4).
While DRM<inline-formula><mml:math id="M361" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> has a constant negative offset when compared to
POLDER, DRM<inline-formula><mml:math id="M362" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> rarely retrieves null AOT values (offsets always
larger than 0; see Table 2). This is likely to be a consequence of the
calibration performed for the DRM<inline-formula><mml:math id="M363" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> method. Also, there is no
obvious correlation between the CALIOP<inline-formula><mml:math id="M364" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> and POLDER
AOT<inline-formula><mml:math id="M365" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> retrievals for all regions.</p>
      <p>Finally, in addition to the 6-month regional study, we also examined the
impact of the vertical aerosol–cloud profiles over the three regions using
data acquired from May to October between 2006 and 2010. We systematically
found higher correlation coefficients between the DRM<inline-formula><mml:math id="M366" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and
POLDER AOTs when the layers were well separated than when they were in
contact (see Table 6). These results have led us to consider the vertical
distribution of aerosols and clouds in the global comparison.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <title>Global analysis on different types of scenes</title>
<sec id="Ch1.S4.SS1">
  <title>Detached, attached, undetermined</title>
      <p>Figure 5a shows the global comparison between the AOT<inline-formula><mml:math id="M367" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> and
AE retrieved with POLDER and DRM<inline-formula><mml:math id="M368" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> for the detached
cases. The AE comparison was only performed when the POLDER AOT at 865 nm
and DRM<inline-formula><mml:math id="M369" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT at 532 nm are larger than 0.1. The colour scales
used in Fig. 5 represent either the POLDER AE<inline-formula><mml:math id="M370" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">670</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">865</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> for the AOT
comparison (Fig. 5a) or the POLDER AOT<inline-formula><mml:math id="M371" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> for the AE
comparison (Fig. 5d). Considering the large amount of selected data
(85.6 % of the two-layer cases) in terms of both spatial and temporal
coverage, the comparison shows a good correlation between the two methods
(<inline-formula><mml:math id="M372" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.68). A better agreement between the methods is found when the
values of DRM<inline-formula><mml:math id="M373" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and POLDER AE are larger than 1.8. This is
likely due to the fact that the POLDER method is more sensitive to fine-mode
aerosols, due to polarization measurements, and also because an improved
description of the fine-mode properties was included in the LUT (i.e. six
fine-mode aerosol models are used).</p>
      <p>Events for which the aerosol layer is attached to the cloud top
represent 14.4 % of the total number of two-layer cases. They are
associated with lower AOT and the correlation between the two retrievals
largely decreases (compared to the detached events). The correlation between
the two AOT retrievals also decreases (<inline-formula><mml:math id="M374" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.36, Fig. 5c). The POLDER
AOT is larger by a coefficient of 1.7 than the DRM<inline-formula><mml:math id="M375" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT on
average. The AE given by both methods is approximately 1.0 (when considering
only AE values associated with AOT <inline-formula><mml:math id="M376" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 0.1). The lateral histogram shows
that the POLDER method identifies AAC events associated with both low and
high AE values, resulting in a mean AE of about 1.0.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T7" specific-use="star"><caption><p>Linear regressions calculated between different methods for data
acquired over June 2006 to December 2010, on a global scale above the ocean
in the case of aerosol attached to the cloud top, detached
from the cloud and undetermined situations for AOT smaller than
1.5.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Linear regressions</oasis:entry>  
         <oasis:entry colname="col2"/>  
         <oasis:entry colname="col3">Detached</oasis:entry>  
         <oasis:entry colname="col4">Attached</oasis:entry>  
         <oasis:entry colname="col5">Undetermined</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">DRM<inline-formula><mml:math id="M377" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> vs. POLDER</oasis:entry>  
         <oasis:entry colname="col2">Slope</oasis:entry>  
         <oasis:entry colname="col3">0.84 <inline-formula><mml:math id="M378" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.003</oasis:entry>  
         <oasis:entry colname="col4">0.59 <inline-formula><mml:math id="M379" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>  
         <oasis:entry colname="col5">0.24 <inline-formula><mml:math id="M380" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.001</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Intercept</oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math id="M381" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.03</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M382" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.001</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math id="M383" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.02</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M384" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.002</oasis:entry>  
         <oasis:entry colname="col5"><inline-formula><mml:math id="M385" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.02</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"><inline-formula><mml:math id="M386" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (COD)</oasis:entry>  
         <oasis:entry colname="col3">0.68</oasis:entry>  
         <oasis:entry colname="col4">0.36</oasis:entry>  
         <oasis:entry colname="col5">0.03</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">DRM<inline-formula><mml:math id="M387" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> vs. POLDER</oasis:entry>  
         <oasis:entry colname="col2">Slope</oasis:entry>  
         <oasis:entry colname="col3">0.78 <inline-formula><mml:math id="M388" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.002</oasis:entry>  
         <oasis:entry colname="col4">0.55 <inline-formula><mml:math id="M389" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.001</oasis:entry>  
         <oasis:entry colname="col5">0.28 <inline-formula><mml:math id="M390" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.001</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Intercept</oasis:entry>  
         <oasis:entry colname="col3">0.10 <inline-formula><mml:math id="M391" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.001</oasis:entry>  
         <oasis:entry colname="col4">0.12 <inline-formula><mml:math id="M392" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.002</oasis:entry>  
         <oasis:entry colname="col5">0.09</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"><inline-formula><mml:math id="M393" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (COD)</oasis:entry>  
         <oasis:entry colname="col3">0.68</oasis:entry>  
         <oasis:entry colname="col4">0.36</oasis:entry>  
         <oasis:entry colname="col5">0.05</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">CALIOP<inline-formula><mml:math id="M394" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> vs. POLDER</oasis:entry>  
         <oasis:entry colname="col2">Slope</oasis:entry>  
         <oasis:entry colname="col3">0.17 <inline-formula><mml:math id="M395" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.002</oasis:entry>  
         <oasis:entry colname="col4">0.12 <inline-formula><mml:math id="M396" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.007</oasis:entry>  
         <oasis:entry colname="col5">0.06 <inline-formula><mml:math id="M397" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.008</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Intercept</oasis:entry>  
         <oasis:entry colname="col3">0.013</oasis:entry>  
         <oasis:entry colname="col4">0.02 <inline-formula><mml:math id="M398" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.001</oasis:entry>  
         <oasis:entry colname="col5">0.14 <inline-formula><mml:math id="M399" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.002</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"><inline-formula><mml:math id="M400" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (COD)</oasis:entry>  
         <oasis:entry colname="col3">0.15</oasis:entry>  
         <oasis:entry colname="col4">0.047</oasis:entry>  
         <oasis:entry colname="col5">0.003</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">CALIOP<inline-formula><mml:math id="M401" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> vs. DRM<inline-formula><mml:math id="M402" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Slope</oasis:entry>  
         <oasis:entry colname="col3">0.17 <inline-formula><mml:math id="M403" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.002</oasis:entry>  
         <oasis:entry colname="col4">0.1 <inline-formula><mml:math id="M404" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.007</oasis:entry>  
         <oasis:entry colname="col5">0.21 <inline-formula><mml:math id="M405" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Intercept</oasis:entry>  
         <oasis:entry colname="col3">0.029</oasis:entry>  
         <oasis:entry colname="col4">0.04 <inline-formula><mml:math id="M406" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.001</oasis:entry>  
         <oasis:entry colname="col5">0.14 <inline-formula><mml:math id="M407" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.001</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"><inline-formula><mml:math id="M408" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (COD)</oasis:entry>  
         <oasis:entry colname="col3">0.15</oasis:entry>  
         <oasis:entry colname="col4">0.03</oasis:entry>  
         <oasis:entry colname="col5">0.01</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><caption><p>Four and a half years of global study on the evolution of POLDER and
DRM<inline-formula><mml:math id="M409" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> above-cloud AOT retrievals as a function of MODIS
effective radius (<inline-formula><mml:math id="M410" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M411" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m) for situations where the
aerosol layer is detached from the cloud top <bold>(a, d)</bold>, for
cases where the aerosol layer is attached to the cloud
top <bold>(b, e)</bold> and for undetermined situations <bold>(c, f)</bold>.
The histograms in <bold>(a)</bold>–<bold>(c)</bold> represent the distribution of
<inline-formula><mml:math id="M412" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. The histograms in <bold>(d)</bold>–<bold>(f)</bold> present the
difference between POLDER and DRM<inline-formula><mml:math id="M413" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> mean AOTs, before the
correction of DRM<inline-formula><mml:math id="M414" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT with <inline-formula><mml:math id="M415" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M416" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">τ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
and after this correction (<inline-formula><mml:math id="M417" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">τ</mml:mi><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mtext>corr.</mml:mtext><mml:mspace width="0.25em" linebreak="nobreak"/><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The
associated tables indicate the number of cases, mean, standard deviation
(<inline-formula><mml:math id="M418" display="inline"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and median values of these differences. The error bars in
<bold>(a)</bold>–<bold>(c)</bold> represent the standard error of the mean (SEM).</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://amt.copernicus.org/articles/10/3499/2017/amt-10-3499-2017-f06.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><caption><p>Same as Fig. 6: POLDER and DRM<inline-formula><mml:math id="M419" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> above-cloud AOT
retrievals as a function of MODIS effective radius (<inline-formula><mml:math id="M420" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M421" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m).</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://amt.copernicus.org/articles/10/3499/2017/amt-10-3499-2017-f07.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><caption><p>Four and a half years of global study of the evolution of POLDER and
DRM<inline-formula><mml:math id="M422" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> above-cloud AOT retrievals, as well as the difference of
these two methods as a function of MODIS cloud optical thickness (COT), for
situations where the aerosol layer is detached from the cloud
top <bold>(a)</bold>, for cases where the aerosol layer is attached to
the cloud top <bold>(b)</bold> and for undetermined
situations <bold>(c)</bold>. The histograms represent the distribution of COT.
The error bars show the standard error of the mean (SEM).
Panels <bold>(d)</bold>–<bold>(f)</bold> display the evolution of
DRM<inline-formula><mml:math id="M423" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT (<inline-formula><mml:math id="M424" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, depolarization ratio
(<inline-formula><mml:math id="M425" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and multiple scattering factor (<inline-formula><mml:math id="M426" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> as a
function of MODIS COT, for the abovementioned situations.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://amt.copernicus.org/articles/10/3499/2017/amt-10-3499-2017-f08.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9"><caption><p>Sensitivity study of lidar ratio (<inline-formula><mml:math id="M427" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, sr) as a function
of the cloud droplets effective radius, using a two-parameter gamma size
distribution in Mie code. The effective variance, <inline-formula><mml:math id="M428" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, is set to
0.088. The real part of the refractive index is fixed to 1.337, while the
imaginary part, <inline-formula><mml:math id="M429" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula>, was set to 0 (blue) and to 0.0001<inline-formula><mml:math id="M430" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> (red).</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://amt.copernicus.org/articles/10/3499/2017/amt-10-3499-2017-f09.pdf"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10" specific-use="star"><caption><p>Median <bold>(a)</bold> and averaged <bold>(b)</bold> backscatter profiles
(km<inline-formula><mml:math id="M431" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> sr<inline-formula><mml:math id="M432" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> for aerosol layer detached from the cloud layer (red)
and aerosols attached to the top of the cloud (blue), for a period of 4.5 years on the global scale. For comparison, the molecular
attenuated backscatter profile is shown as a green line. The data were filtered
for a cloud top altitude lower than 1.5 km, a cloud optical thickness (COT)
larger than 5 and for a DRM<inline-formula><mml:math id="M433" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT at 532 nm larger than 0.1.
The number of 5 km horizontal-resolution pixels is also shown. The mean,
standard deviation (<inline-formula><mml:math id="M434" display="inline"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and median of aerosol top altitude (ATA),
aerosol base altitude (ABA) and cloud top altitude (CTA) are given for each
situation. Same values are shown for POLDER AOT at and DRM<inline-formula><mml:math id="M435" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>
AOT at 532 nm.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/10/3499/2017/amt-10-3499-2017-f10.png"/>

        </fig>

      <?xmltex \floatpos{p}?><fig id="Ch1.F11"><caption><p>Sensitivity study of polarized radiance at 865 nm to the relative
position of the aerosol layer above the cloud. Simulation performed for a
cloud layer located between 0 and 1 km and aerosol layers varying at
different altitudes. The cloud droplet effective radius is fixed to
10 <inline-formula><mml:math id="M436" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m and the effective variance is 0.08. The aerosol layer is
characterized by an AOT of 0.25 at 865 nm, a refractive index of
<inline-formula><mml:math id="M437" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.47</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:math></inline-formula> and an aerosol effective radius of 0.15 <inline-formula><mml:math id="M438" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://amt.copernicus.org/articles/10/3499/2017/amt-10-3499-2017-f11.png"/>

        </fig>

      <p>The undetermined situations correspond to retrievals when CALIOP
does not give all the information regarding the layer altitudes. The number
of cases is significant (approximately 92 % of the total number of global
retrievals) but most of data (95 %) correspond to AOT<inline-formula><mml:math id="M439" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula>
lower than 0.2. This probably explains why the layer detection algorithm has
difficulties in estimating the base and top of the aerosol layer. For the
undetermined cases, we observe that there is not much correlation
between POLDER and DRM<inline-formula><mml:math id="M440" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> measurements. On average, the
DRM<inline-formula><mml:math id="M441" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOTs are centred around zero for this category whereas
POLDER has a non-negligibly low AOT for most cases. In this category, the AE
comparison shows a better consistency between the methods for
AOT<inline-formula><mml:math id="M442" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> and for AE of approximately 2.0.</p>
      <p>Table 7 shows the results of the linear regressions performed between the
AOTs retrieved with POLDER and the other active
methods considered in our study for
each category (i.e. detached, attached and undetermined). We recapture the
systematically larger offsets of DRM<inline-formula><mml:math id="M443" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> AOT<inline-formula><mml:math id="M444" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula>
compared to DRM<inline-formula><mml:math id="M445" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and the underestimation of
CALIOP<inline-formula><mml:math id="M446" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">OM</mml:mi></mml:msub></mml:math></inline-formula> AOT with respect to the other methods.</p>
</sec>
<sec id="Ch1.S4.SS2">
  <title>Evolution of the above-cloud AOT retrievals with cloud
properties</title>
      <p>In principle, the retrieval of AAC properties from the methods considered in
this study should not depend on the properties of the underlying clouds.
However, hypotheses and empirical relations used in the retrieval methods to
exploit the signal backscattered by the underlying cloud cover obviously have
their limitations. In order to understand potential issues linked with
diversity of cloud properties, we analyse in this section the difference
between the AOT retrievals of POLDER, DRM<inline-formula><mml:math id="M447" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and
DRM<inline-formula><mml:math id="M448" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> by classes of cloud properties (COT and <inline-formula><mml:math id="M449" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
retrieved with MODIS). We considered global measurements acquired for 4.5 years of data and used the classification defined in Sect. 2.3.2.</p>
      <p>Figure 6 presents POLDER and DRM<inline-formula><mml:math id="M450" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT<inline-formula><mml:math id="M451" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">532</mml:mn></mml:msub></mml:math></inline-formula> retrievals as a
function of the MODIS droplets effective radius (<inline-formula><mml:math id="M452" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, while
Fig. 8 displays POLDER and DRM<inline-formula><mml:math id="M453" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT<inline-formula><mml:math id="M454" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> as a
function of the MODIS COT. Histograms of the cloud
properties are also reported in Figs. 6, 7 and 8. The results of the POLDER
and DRM<inline-formula><mml:math id="M455" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> AOT<inline-formula><mml:math id="M456" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">532</mml:mn></mml:msub></mml:math></inline-formula> comparison as a function of the effective
radius are shown in Fig. 7. DRM<inline-formula><mml:math id="M457" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and DRM<inline-formula><mml:math id="M458" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula>
AOT<inline-formula><mml:math id="M459" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> generally exhibit rather similar behaviour, at least
qualitatively. Therefore, we did not report the results found for the
DRM<inline-formula><mml:math id="M460" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> AOT<inline-formula><mml:math id="M461" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">532</mml:mn></mml:msub></mml:math></inline-formula> as a function of MODIS COT.</p>
<sec id="Ch1.S4.SS2.SSS1">
  <?xmltex \opttitle{AOT vs. $r_{\mathrm{eff}}$}?><title>AOT vs. <inline-formula><mml:math id="M462" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></title>
      <p>The lateral histograms plotted in Figs. 6 and 8 show that most of the AAC
scenes correspond to cloud droplets effective radius values between 8 and
15 <inline-formula><mml:math id="M463" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m (mean <inline-formula><mml:math id="M464" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> equal to 12 <inline-formula><mml:math id="M465" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m) and COT
ranging from 5 to 15 (mean COT of 10). These mean values are expected since
most of the of AAC events are generally associated with low-level
non-precipitating clouds, such as stratocumulus ones, which typically show
rather small droplets (approximately 10 <inline-formula><mml:math id="M466" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m) and optical thickness
values of approximately 10.</p>
      <p>Figure 6a shows the POLDER and DRM<inline-formula><mml:math id="M467" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOTs for the detached
situations. For the two methods, the retrieved AOTs are maximal for the
smallest values of <inline-formula><mml:math id="M468" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and progressively decrease with
<inline-formula><mml:math id="M469" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Same tendencies are observed for the DRM<inline-formula><mml:math id="M470" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> (see
Fig. 7a). The two curves have an offset, however. The histogram of the
differences between POLDER and DRM<inline-formula><mml:math id="M471" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT (<inline-formula><mml:math id="M472" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">τ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is
presented in Fig. 6d. The mean <inline-formula><mml:math id="M473" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> value computed over the entire
range of <inline-formula><mml:math id="M474" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is equal to 0.073. This offset is not constant and
slightly increases with <inline-formula><mml:math id="M475" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, suggesting a sensitivity of one of
the two methods to the cloud droplets effective radius. The DRM algorithm
does not use an explicit parameterization of the lidar ratio as a function of
the cloud droplets effective radius. An implicit dependence will arise from
the latitudinal correction (Eq. 9) when clouds at different latitudes exhibit
different microphysical properties. In order to understand the usefulness of
adding an explicit parameterization, we recalculated the DRM<inline-formula><mml:math id="M476" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>
AOT<inline-formula><mml:math id="M477" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula>, taking into account the dependence of <inline-formula><mml:math id="M478" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
on <inline-formula><mml:math id="M479" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. This calculation assumes a simplified and unique droplet
size distribution and is based on MODIS <inline-formula><mml:math id="M480" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> retrieval. We expect
that even if the cloud droplet size distribution is variable (Miles et al.,
2000) and the ACAOT creates a bias in <inline-formula><mml:math id="M481" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the results will still provide
guidance for future algorithm development. As defined in Josset et
al. (2011), <inline-formula><mml:math id="M482" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was computed using a Mie code with the following
equation:
              <disp-formula id="Ch1.E11" content-type="numbered"><mml:math id="M483" display="block"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">4</mml:mn><mml:mi mathvariant="italic">π</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">ω</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">180</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M484" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">180</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the average value of the phase function in the
backscatter direction computed over the size distribution. <inline-formula><mml:math id="M485" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ω</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is
the SSA of the particles, defined as the ratio between
the mean scattering coefficient and the mean extinction coefficient computed
over the particle size distribution. We used a two-parameter gamma size
distribution with an effective variance of 0.088. The real refractive index
was set to 1.337. Liquid water droplets do not significantly absorb at
532 nm and the imaginary part of the complex refractive index was set to 0.
As shown in Fig. 9, <inline-formula><mml:math id="M486" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> slightly decreases with <inline-formula><mml:math id="M487" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
from 19.5 to 15.5 as the effective radius values increases from 5 to
40 <inline-formula><mml:math id="M488" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m. With this correction, the mean difference between POLDER and
the DRM<inline-formula><mml:math id="M489" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT<inline-formula><mml:math id="M490" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> (<inline-formula><mml:math id="M491" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">corr</mml:mi><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. 6d) decreases from 0.073 to 0.065. We found equivalent
results for the attached and undetermined cases (Fig. 6b
and c). After correction of <inline-formula><mml:math id="M492" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the difference between POLDER and
DRM<inline-formula><mml:math id="M493" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> decreases on average by 0.01 for the attached
cases and by 0.019 for the undetermined cases. We also observe that
most of the negative AOT values retrieved by the DRM<inline-formula><mml:math id="M494" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> shift
either to null values or weakly positive values when this correction is
included (Fig. 6a–c). We are aware that MODIS effective radius may be
affected by the presence of aerosols above clouds. For example, Haywood et
al. (2004) found biases of <inline-formula><mml:math id="M495" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>2 <inline-formula><mml:math id="M496" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m for <inline-formula><mml:math id="M497" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in case
of strong dust events above clouds and Meyer et al. (2015) found an increase
in the <inline-formula><mml:math id="M498" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> monthly mean of 2 % in case of above-cloud
absorbing aerosols. We expect that large biases on <inline-formula><mml:math id="M499" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> could be
possible in case of high aerosol loading for detached cases.
However, we consider that the impact of the biases on the retrieved
<inline-formula><mml:math id="M500" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> on our findings and conclusions can be neglected, since the
analysis hold for (i) a wide range of droplets effective radius (from 5 to
40 <inline-formula><mml:math id="M501" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m) and (ii) AAC events associated with low aerosol loadings
(see the results for the undetermined cases), where the impacts of
the aerosols on the cloud retrievals are expected to be minimized or
negligible.</p>
</sec>
<sec id="Ch1.S4.SS2.SSS2">
  <title>AOT vs. COT</title>
      <p>The two methods were developed to detect AAC events in the case of optically
thick and homogeneous liquid water clouds. In the following, we only discuss
results obtained for large values of COT (larger than 5). If the clouds are
optically thinner, the two methods are potentially less accurate since they
become sensitive to the surface contribution. Hu et al. (2007a) noticed the
surface impact on DRM<inline-formula><mml:math id="M502" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> when the underlying cloud is not entirely
opaque; therefore the assumptions used in the DRM<inline-formula><mml:math id="M503" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> AOT
retrievals are not met. For COTs ranging between 5 and 30 and for
detached cases, the POLDER AOTs are almost constant and reach 0.3 on
average at 532 nm (see Fig. 8a). Most of the associated COT values then
range between 5 and 10. For these cases, DRM<inline-formula><mml:math id="M504" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and POLDER
AOTs are offset by around 0.07 on average, as noted above. However, the
DRM<inline-formula><mml:math id="M505" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT progressively increases with the COT, which is not
observed for the POLDER AOT. Consequently, the differences in AOT between the
two methods become almost negligible for the largest (and less frequent)
values of COT (larger than 20). For COTs larger than 3, the polarized signal
reflected by the cloud is saturated and the POLDER method should be
insensitive to COT. DRM<inline-formula><mml:math id="M506" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> is sensitive to the multiple
scattering processes occurring within the cloud layers and might be impacted
by the COT since multiple scattering increases with the optical thickness.
The measured depolarization (<inline-formula><mml:math id="M507" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and the multiple scattering factor
(<inline-formula><mml:math id="M508" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">calibr</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> plotted as a function of the COT are shown in
Fig. 8d. As expected, the depolarization and the multiple scattering factor
respectively increase and decrease as COT increases. The increase in the
DRM<inline-formula><mml:math id="M509" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT observed at large COTs might be due to an increase in
the multiple scattering. We recall that DRM<inline-formula><mml:math id="M510" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> uses a
relationship to connect the depolarization and the multiple scattering factor
and that this relation is calibrated based on CALIOP data. The calibration
might be less accurate in the case of AAC events associated with clouds for which
the properties are statistically less representative. Again, we presume that
our conclusions are not impacted by the fact that the MODIS COTs can be
potentially biased in case of AAC events since the tendencies we observed
hold for a large range of variability in COT (5 to 30) and also for AAC
events associated with low AOT above clouds (see the results for the
undetermined cases).</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S5">
  <title>Discussion</title>
      <p>In the first part of this section, we quantify and discuss the overall
differences found between the active and passive methods in terms of the
retrieved AOT. In the second part, we address more specifically the
attached cases and make hypotheses regarding the meaning of these
results.</p>
      <p>On average, the difference between POLDER and DRM<inline-formula><mml:math id="M511" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOTs at
532 nm is equal to 0.073 for the detached cases and 0.087 for the
undetermined cases. These differences slightly decrease to 0.065 and
0.068, respectively, when we account for the dependency of the cloud droplets
lidar ratio (<inline-formula><mml:math id="M512" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M513" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in Eq. (10). The POLDER AOTs
are systematically smaller than the ones retrieved with DRM<inline-formula><mml:math id="M514" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula>. On
average, these differences between these two methods are equal to <inline-formula><mml:math id="M515" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.039</mml:mn></mml:mrow></mml:math></inline-formula>
and <inline-formula><mml:math id="M516" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.057</mml:mn></mml:mrow></mml:math></inline-formula>, for the detached cases, and reach <inline-formula><mml:math id="M517" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.036</mml:mn></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M518" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.048</mml:mn></mml:mrow></mml:math></inline-formula> for the undetermined cases, respectively without and with
corrections for <inline-formula><mml:math id="M519" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Thereby, the POLDER AOT estimates range, on
average, between the DRM<inline-formula><mml:math id="M520" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> and DRM<inline-formula><mml:math id="M521" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> ones. The
differences in AOTs found between the POLDER method and the two DRM ones
could be set to zero by modifying the lidar calibration by roughly
<inline-formula><mml:math id="M522" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>10 %. One another main difference between the three methods is their
different responses in terms of AOT when the atmosphere above the clouds
becomes pristine. The majority of AOT (94 %) is lower than 0.1 at 865 nm
for the undetermined cases. For these cases, the POLDER algorithm
retrieves a mean AOT of about 0.04 at 865 nm. The accuracy of the POLDER AOT
product is on the same order of magnitude. For an AOT<inline-formula><mml:math id="M523" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">865</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> of
0.2, the error for a real refractive index uncertainty of <inline-formula><mml:math id="M524" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>0.06 would be
about 0.05; for an imaginary refractive index uncertainty of <inline-formula><mml:math id="M525" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>0.01, the
error would be of 0.02 (Peers et al., 2015). The impact of the assumed
refractive index is lower at smaller AOT (especially for an AOT of 0.04). The
background of the extrapolated POLDER AOT at 532 nm for the undetermined
cases reaches 0.09. This latter value is only reported for the sake of
comparison with the two other methods since the Ångström exponent
retrieved by POLDER (and consequently the AOT extrapolated at 532 nm)
cannot be accurately retrieved for low AOTs. DRM<inline-formula><mml:math id="M526" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> found a mean
AOT of about 0.005 at 532 nm for the undetermined cases (see Fig. 6c). The
result is likely due to the re-calibration process since DRM<inline-formula><mml:math id="M527" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula>
found a background even larger than that of  POLDER: about 0.12 at 532 nm.
It is difficult to assess the truthfulness of this background, considering
the given level of accuracy of the POLDER method and the uncertainties
associated with the lidar calibration. We assume that these background values
are not physical and could be due to some inherent limitations of the
retrieval methods. From our data, however, we cannot exclude the possibility
that there is always a background loading of particles above clouds (e.g.
aerosols or fine droplets in formation). Nevertheless, the main result of our
investigation is that POLDER and DRM methods compare well for most situations
with a mean difference of about <inline-formula><mml:math id="M528" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>0.07 in AOT at 532 nm.</p>
      <p>Although the number of cases is small, the results of the attached cases
are interesting. They suggest that the lidar CALIOP and POLDER could be
affected by layers of aerosols that physically and locally interact with the
upper part of the cloud. In order to understand how the vertical profiles
differ from one situation to another, we compared the CALIOP attenuated
backscatter coefficient for attached and detached cases. We considered
the period 2006–2010 and used data acquired over the entire globe. We only
select the attached and detached cases where the cloud top altitude is
below 1.5 km, the COT is larger than 5 and the DRM<inline-formula><mml:math id="M529" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>
AOT<inline-formula><mml:math id="M530" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> is larger than 0.1. These criteria allow for selection
of data that correspond to AAC events associated with similar cloud vertical
extents and with significant AOTs. For these cases, we computed the average
and median of the CALIOP level 1 attenuated backscatter coefficients at
532 nm. Figure 10 presents these results and some information concerning the
mean and median values of CALIOP level 2 products: cloud top altitude,
aerosol layer's base and top altitudes. The mean and median values computed
for the AOTs retrieved by POLDER and DRM<inline-formula><mml:math id="M531" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> and the numbers of
sampled events are also reported. Two different types of profiles can be
observed for the detached and attached situations. For the detached
cases, the aerosol and cloud backscattering profiles can be easily
distinguished in both the median and mean profiles. The strong peaks in the
backscatter profiles at around 1 km correspond to the top of the clouds,
whereas the increase in the lidar backscatter signal observed between 2 and
4 km in altitude comes from the aerosols. For the attached situations, the
backscatter profiles are noisier, which is likely due to the fact that the
number of detected events is smaller compared to detached cases. The top of
the cloud layer is still clearly visible in the mean and median backscattered
lidar signals, but two maxima can be observed. We assume that we sampled two
different regimes of clouds. In addition, there is a continuous transition in
the backscatter signal between the top of the cloud and the above molecular
atmosphere that is most clearly visible in the median profiles. This signal
does not appear for the detached cases. This signal could explain the
non-negligible above-cloud AOTs retrieved by POLDER and DRM<inline-formula><mml:math id="M532" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>
for the attached cases (see Fig. 5). It is difficult to assess the origin
of the signal.
It might be due to aerosols
layers that penetrate the cloud layers at the top of the clouds. Natural
aerosol or fine droplets in formation, commonly present in the vicinity of
the clouds, might also create this additional signal.</p>
      <p>Another hypothesis that could explain the low AOT correlation for the
attached cases is that the aerosols located within the cloud layer
could affect the polarized radiances measured by POLDER. Note that the
polarized radiance at 865 nm is not affected by the vertical position of the
aerosol layer as long as there is no contact between the aerosol and the
cloud. Since the operational algorithm developed for POLDER assumes that the
entire aerosol layer is located above the clouds, an additional polarized
signal coming from aerosol located within the cloud would lead to an
overestimation of the above-cloud AOT retrieved from POLDER. To test this
assumption, we modelled the polarized radiance measured by POLDER for AAC
scenes, considering different vertical locations of the aerosol layer
(Fig. 11). We used the SOS radiative
transfer code (Lenoble et al., 2007) for this simulation. We considered a
liquid water cloud located between 0 and 1 km. The particles (aerosol and
cloud) are vertically homogeneously mixed. The COT is equal to 10 and the
effective radius and variance are equal to 10 <inline-formula><mml:math id="M533" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m and 0.08,
respectively. The aerosol layer is characterized by an AOT of 0.25 at
865 nm, a refractive index of <inline-formula><mml:math id="M534" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.47</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:math></inline-formula> and an effective radius of
0.15 <inline-formula><mml:math id="M535" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m. Figure 11 shows the typical polarized feature for AAC
events in case of detached situations (i.e. aerosols located between
1.25 and 1.75 km): a creation of polarization is observed at side and
forward scattering angles, whereas the cloud bow magnitude decreases. For the
attached case (aerosols between 0.75 and 1.25 km), the amount of
polarization created at forward scattering angles decreases and the cloud bow
attenuation is less significant in comparison with the detached
scenario. When the aerosol layer is located within the upper part of the
cloud layer (between 0.5 and 1 km) we still observe a weak polarized signal
created at forward scattering angles. When the aerosol layer is located in
the lower part of the cloud layer, the effects of the aerosols disappear
since the polarized radiance scattered by the aerosols is lost due to
multiple scattering occurring within the clouds. These simulations were
processed with the POLDER algorithm (Waquet et al., 2013b). We recall that
the LUTs used in this algorithm were built for detached situations.
The algorithm retrieved an AOT of 0.09 at 865 nm when the aerosols are
located within the upper part of the cloud layer. This demonstrates that
polarized radiances are sensitive to aerosols situated within the
clouds for the attached cases.</p>
      <p>The DRM methods might also be impacted by the presence of aerosols within the
clouds. Aerosols as a solution within the cloud droplets (i.e. internal
mixture) might impact the chemical composition of the droplets and modify
their ability to backscatter light. Figure 9 shows lidar ratio computed for
absorbing cloud droplets. We used an imaginary part of 0.0001 for the complex
refractive index of the droplets. This might simulate, for instance, the
properties of brown clouds contaminated by absorbing aerosols. The chosen
value is in agreement with the refractive indices given for water containing
soot inclusions with volume fractions ranging between 10<inline-formula><mml:math id="M536" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and 10<inline-formula><mml:math id="M537" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
(Erlick, 2006). We observe a drastic increase of <inline-formula><mml:math id="M538" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> with
<inline-formula><mml:math id="M539" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (from 21.7 sr at 5 <inline-formula><mml:math id="M540" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m to 50 sr at
40 <inline-formula><mml:math id="M541" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m) when the water droplet is weakly absorbing. In the case of
an external mixture, we assume that the presence of aerosols at the top of
cloud might also modify the value of <inline-formula><mml:math id="M542" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Any deviation from the
19 sr value assumed for the droplets lidar ratio in Eq. (9) will
necessarily impact the retrieved AOT and the differences observed between the
AOT estimates provided by the POLDER and DRM methods.</p>
</sec>
<sec id="Ch1.S6" sec-type="conclusions">
  <title>Conclusions</title>
      <p>In this study, we compared and analysed the consistency of the AOT and AE
retrievals above clouds from different passive and active techniques. We used
the CALIOP operational algorithm (Winker et al., 2009), the POLDER
polarization method (Waquet et al., 2013b) and the CALIOP-based
depolarization ratio method (DRM<inline-formula><mml:math id="M543" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (Hu et al., 2007a), for
which we proposed a re-calibrated version of the DRM algorithm
(DRM<inline-formula><mml:math id="M544" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The observations were made for (a) three case studies
corresponding to an African biomass-burning event, a Saharan dust event and a
Siberian biomass-burning event; (b) a regional-scale analysis over South
Atlantic Ocean, North Atlantic Ocean and North Pacific Ocean for a period of
6 months in 2008; and (c) a global-scale analysis for different vertical
layer distributions for the period 2006–2010.</p>
      <p>In the regional analysis, we observed that POLDER method and DRM are in good
agreement when the microphysics of aerosols is dominated by fine-mode
particles of biomass-burning aerosols (in the South Atlantic region, <inline-formula><mml:math id="M545" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.83)
or coarse-mode aerosols of dust (in the North Atlantic region,
<inline-formula><mml:math id="M546" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.82). A good correlation between these methods (<inline-formula><mml:math id="M547" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.68)
is also noticed in the global treatment, when the aerosol and cloud
layers are well separated. Nevertheless, some of the detached cases
considered in our study, mainly the ones associated with optically thick
smoke layers, are likely to be incorrectly classified as detached.
As a future perspective, these misclassified detached cases (due to strong
attenuation of the CALIOP 532 nm signal) could be detected by controlling
the CALIOP 1064 nm signal, which was shown to provide more sensitivity to
the entire vertical extent of these absorbing aerosol layers. The CALIOP
operational method largely underestimates the AOT above clouds in all
situations, with respect to other methods.</p>
      <p>The differences between the DRM and POLDER retrievals increase when a complex
mixture of aerosols is expected (such as in the East Asia region). This is
probably due to the fact that the current algorithm developed for POLDER uses
a limited number of microphysical models of aerosols. Also, the relative
position of the aerosol layer above the cloud impacts the AOT retrievals from
both active and passive measurements: the correlation decreases when the
layers are in contact (<inline-formula><mml:math id="M548" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.36), suggesting that aerosols at the
top or within the cloud can affect the AOT retrievals. One hypothesis is that
an additional polarized signal coming from aerosol located within
the cloud could affect the polarization signal and method, which leads to an
overestimation of the AOT retrieved with POLDER algorithm. The aerosols
attached with or within the cloud also have the potential
to impact the DRM retrievals by modifying the lidar ratio (and consequently
the AOT) as a result of internal or external mixture.</p>
      <p>Furthermore, we investigated potential biases in the retrieved AOT measured
by POLDER and DRM<inline-formula><mml:math id="M549" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> as a function of MODIS cloud properties
(i.e. droplet effective radius (<inline-formula><mml:math id="M550" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and COT). The tendencies show an increase in the difference between the two
methods for larger <inline-formula><mml:math id="M551" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, suggesting sensitivity to the cloud
droplet effective radius. For this reason, we recalculated the
DRM<inline-formula><mml:math id="M552" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula> AOT<inline-formula><mml:math id="M553" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula>, taking into account the dependence of lidar
ratio on <inline-formula><mml:math id="M554" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, as this method assumes a constant lidar ratio
regarding the droplet effective radius. By doing so, we observed a decrease
in the difference between POLDER and DRM methods and a shift of the DRM AOT
values from negative to positive. For a better accuracy of DRM retrievals in
future studies, this correction should be taken into account. The results
show also that the multiple scattering processes, which are more pronounced
in optically thick clouds, could also affect the DRM technique.</p>
      <p>All of the aforementioned situations have revealed that DRM<inline-formula><mml:math id="M555" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> has
larger mean AOT than that of DRM<inline-formula><mml:math id="M556" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>. This is likely to be a
consequence of the re-calibration performed for the DRM<inline-formula><mml:math id="M557" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>
method. Actually, POLDER AOT<inline-formula><mml:math id="M558" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">532</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula> values are consistently smaller than
the ones of DRM<inline-formula><mml:math id="M559" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Hu</mml:mi></mml:msub></mml:math></inline-formula> and larger than those of DRM<inline-formula><mml:math id="M560" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">SODA</mml:mi></mml:msub></mml:math></inline-formula>.
The primary conclusion of our investigation is that POLDER and DRM techniques
are comparable for the majority of cases, with a mean difference of about
<inline-formula><mml:math id="M561" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>0.07 in AOT at 532 nm, depending on lidar calibration.</p>
      <p>Given the fact that each method relies upon different physical concepts,
applied to different sensors and measurements, the high value of the
correlation obtained for the AOT retrievals is a remarkable result that
highlights the coherence between active and passive methods for aerosols
above clouds. Nonetheless, more efforts have to be done to increase the
accuracy of the methods in order to better understand aerosols above clouds
and their related effects. Airborne measurements are extremely useful in
providing information on aerosols' above-cloud properties. Several ongoing
and planned airborne field campaigns will attempt to characterize the
properties of biomass-burning aerosols over the South Atlantic Ocean
(Zuidema et al., 2016). Planned measurements from the French
Falcon 20 aircraft, equipped with a high-resolution lidar, an airborne
sun photometer and a POLDER-like sensor, will notably be considered for a
future validation of CALIOP DRM and POLDER above-cloud aerosol products.
Another perspective is to improve the POLDER algorithm by introducing
additional dust or mixture models with larger or smaller effective radii
values in the LUT. This would definitely improve the AOT and AE retrievals
in more complex situations (such as East Asia region). Also, our results
suggest that a combination of POLDER and DRM methods has the potential to
detect aerosols within clouds. It is very relevant to study these situations,
since they can affect the retrievals and provide important information
regarding the cloud processes. A further perspective would be to exploit the
synergy between CALIOP and POLDER to infer the direct aerosol radiative
forcing, aerosol heating rates and the semi-direct effect of absorbing
aerosols located above clouds.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability">

      <p>All data are available at ICARE website on-line archive:
<uri>http://www.icare.univ-lille1.fr/archive</uri>.</p>
  </notes><notes notes-type="competinginterests">

      <p>The authors declare that they have no conflict of
interest.</p>
  </notes><ack><title>Acknowledgements</title><p>Lucia Deaconu's grant is provided by the CaPPA project (Chemical and
Physical Properties of the Atmosphere), which is funded by the French
National Research Agency (ANR) through the PIA (Programme d'Investissement
d'Avenir) under contract ANR-11-LABX-0005-01 and by the Regional Council
Hauts-de-France and the European Funds for Regional Economic
Development (FEDER).<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>
Edited by: Piet Stammes<?xmltex \hack{\newline}?>
Reviewed by: Hiren Jethva and two anonymous referees</p></ack><ref-list>
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    <!--<article-title-html>Consistency of aerosols above clouds characterization from A-Train active and passive measurements</article-title-html>
<abstract-html><p class="p">This study presents a comparison between the retrieval of optical properties
of aerosol above clouds (AAC) from different techniques developed for the
A-Train sensors CALIOP/CALIPSO and POLDER/PARASOL. The main objective is to
analyse the consistency between the results derived from the active and the
passive measurements. We compare the aerosol optical thickness (AOT) above
optically thick clouds (cloud optical thickness (COT) larger than 3) and
their Ångström exponent (AE). These parameters are retrieved with the
CALIOP operational method, the POLDER operational polarization method and the
CALIOP-based depolarization ratio method (DRM) – for which we also propose a
calibrated version (denominated DRM<sub>SODA</sub>, where SODA is the
Synergized Optical Depth of Aerosols). We analyse 6 months of data over three
distinctive regions characterized by different types of aerosols and clouds.
Additionally, for these regions, we select three case studies: a
biomass-burning event over the South Atlantic Ocean, a Saharan dust case over
the North Atlantic Ocean and a Siberian biomass-burning event over the North
Pacific Ocean. Four and a half years of data are studied over the entire
globe for distinct situations where aerosol and cloud layers are in contact
or vertically separated. Overall, the regional analysis shows a good
correlation between the POLDER and the DRM<sub>SODA</sub> AOTs when the
microphysics of aerosols is dominated by fine-mode particles of
biomass-burning aerosols from southern Africa (correlation coefficient
(<i>R</i><sup>2</sup>) of 0.83) or coarse-mode aerosols of Saharan dust (<i>R</i><sup>2</sup> of 0.82).
A good correlation between these methods (<i>R</i><sup>2</sup> of 0.68) is also observed
in the global treatment, when the aerosol and cloud layers are separated
well. The analysis of detached layers also shows a mean difference in AOT of
0.07 at 532 nm between POLDER and DRM<sub>SODA</sub> at a global scale. The
correlation between the retrievals decreases when a complex mixture of
aerosols is expected (<i>R</i><sup>2</sup> of 0.37) – as in the East Asia region – and
when the aerosol–cloud layers are in contact (<i>R</i><sup>2</sup> of 0.36). The
correlation coefficient between the CALIOP operational method and POLDER is
found to be low, as the CALIOP method largely underestimates the aerosol
loading above clouds by a factor that ranges from 2 to 4.</p><p class="p">Potential biases on the retrieved AOT as a function of cloud properties are
also investigated. For different types of scenes, the retrieval of
above-cloud AOT from POLDER and from DRM are compared for different
underlying cloud properties (droplet effective radius (<i>r</i><sub>eff</sub>) and
COT retrieved with MODIS). The results reveal that DRM AOT vary with
<i>r</i><sub>eff</sub>. When accounting for <i>r</i><sub>eff</sub> in the DRM algorithm,
the consistency between the methods increases. The sensitivity study shows
that an additional polarized signal coming from aerosols located
<i>within</i> the cloud could affect the polarization method, which leads
to an overestimation of the AOT retrieved with POLDER algorithm. In addition,
the aerosols <i>attached</i> to or <i>within</i> the cloud can potentially
impact the DRM retrievals through the modification of the cloud droplet
chemical composition and its ability to backscatter light. The next step of
this work is to combine POLDER and CALIOP to investigate the impacts of
aerosols on clouds and climate when these particles are transported above or
within clouds.</p></abstract-html>
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